Here's what the chart looks like before we put any of We know that Bill does 1/2 reports per hour. Jacob is canoeing in a river with a 5 mph current. The integer pair {5, 28} has product 140 and sum 23. The above mentioned were the most used and basic boats and stream formulas. Going upstream, Distance = (Rate)(Time), so 16 = (B-C)(2) How many hours would it take Jean if she worked alone? The sum of a number and its reciprocal is \(\frac{41}{20}\). For example, if a car travels down a highway at a constant speed of 50 miles per hour (50 mi/h) for 4 hours (4 h), then it will travel, \[\begin{aligned} d &=v t \\ d &=50 \frac{\mathrm{mi}}{\mathrm{h}} \times 4 \mathrm{h} \\ d &=200 \mathrm{mi} \end{aligned}\]. She paddles 3 miles upstream against the current and then returns to the starting location. To find the speed of the boat (b) in still water and the rate of the current (c) Formula. But the boat is not on a still lake; The speed of the current is miles per hour. Find the rate of the current and the rate of the boat in still water. so we have 2 equations which must be solved . Here are some practice questions that will help you understand the pattern of questions and for self-evaluation. Solution. Suppose that he can canoe 4 miles upstream in the same amount of time as it takes him to canoe 8 miles downstream. 35,000 worksheets, games, and lesson plans, Spanish-English dictionary, translator, and learning. Denote the speed of the boat by v and the speed of the current by w. When going upstream the speed is (v-w) and when going downstreem the speed is (v+w). Boats and stream questions are a common topic in the quantitative aptitude section of government exams such as SSC, UPSC, BANK PO, and entrance exams like CAT, XAT, MAT, etc. Add to folder More answers below Quora User So after 5 hours, the distance traveled upstream would be 5(y-x) . answered 11/14/20, Mathematics Teacher - NCLB Highly Qualified. a. Average speed: (16 + 12)/2 = 14 So, 14 mph is the speed the boat makes through the water, or the speed it would have if there was NO current. Then the speed of train B is at a rate of B miles per hour. Find the number(s). On the return trip, the boat benefits from the current, so its net speed on the return trip is 32 + c miles per hour. If the boat is traveling The boat travels downstream 150 miles at a net speed of 40 miles per hour. Let x be the distance to Boston. Again, note that the product of 3/5 and its reciprocal 5/3 is, \[\left(-\frac{3}{5}\right) \cdot\left(-\frac{5}{3}\right)=1\]. it will become 12 = B+C. Let's see what kinds of equations we can come up with. Round your answer to the nearest hundredth. Accessibility StatementFor more information contact us atinfo@libretexts.orgor check out our status page at https://status.libretexts.org. While returning because of water resistance, it took 1 hour 15 minutes to cover the same distance. Find the speed of the current and the speed of the boat in still water. The same boat can travel 36 miles downstream in 3 hours. Emily can paddle her canoe at a speed of 2 mph in still water. Find out how you can intelligently organize your Flashcards. We start by recalling the definition of the reciprocal of a number. Lets look at another application of the reciprocal concept. Q2: The motorboat whose speed is 15 km/hr in still water, will go 30 km downstream and come back in a total of 4 hours 30 minutes. This leads to the result, \[\frac{60}{3-c}=2\left(\frac{60}{3+c}\right)\]. Then. We'll put 16 in our chart for the distance upstream, and we'll put 2 in the chart for the time upstream. Time going + Time returning = Total time. That is, Bill will complete 2/3 of a report. How many hours will it take if they work together? It will take 30 hours to travel 60 miles at this rate. How many hours would it take Amelie if she worked alone? A link to the app was sent to your phone. Upstream- When the boat is flowing in the opposite direction of the stream, it is called Upstream. Next Lesson: Radicals: Rational and irrational numbers. \[\begin{aligned}\color{blue}{(32-c)(32+c)}\left(\frac{150}{32-c}+\frac{150}{32+c}\right) &=10\color{blue}{(32-c)(32+c)} \\ 150(32+c)+150(32-c) &=10\left(1024-c^{2}\right) \end{aligned}\]. Because it takes them 12 hours to complete the task when working together, their combined rate is 1/12 kitchens per hour. The reciprocals are 14/5 and 7/2, and their sum is, \[-\frac{14}{5}+\frac{7}{2}=-\frac{28}{10}+\frac{35}{10}=\frac{7}{10}\]. We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. Australia, Leverage Edu Tower, What proportion of the kites are blue? Using the equation speed = distance/time: 12 miles upstream take 1.5 hours, so v-w=12/1.5=24/3=8 m/h, 24 miles downstream take 1.5 hours as well, so v+w=24/1.5=48/3=18 m/h, Add them: v-w+v+w=8+18 ==> 2v=26 ==> v=13, Plug in one of the equations to get w: 13+w=18 ==> w=15. The boat travels at miles per hour in still water. If the speed of the boat in still water is 15 miles per hour, what is the speed of the current? It takes Amelie 9 hours to paint the same room. A student gave 2/3 of her cassette tapes to her friend. Again, it is very important that we check this result. Please upgrade to Cram Premium to create hundreds of folders! To set up an equation, we need to use the fact that the time to travel upstream is twice the time to travel downstream. What was the interest rate on the loan? How much time will it take to come back? rate and time that the boat travels going both upstream and downstream. What is the speed (in mph) of the current? Note that each row of Table \(\PageIndex{1}\) has two entries entered. A-258, Bhishma Pitamah Marg, How long is the flag if its width is 5 feet? The speed of a freight train is 20 mph slower than the speed of a passenger train. Note that ac = (1)(84) = 84. Then the speed of boat in still water and the speed of current are respectively. Introducing Cram Folders! 2700 = ________________ 4. answered 02/17/15. For example, in the first row, d = 60 miles and v = 3 c miles per hour. The speed of a boat in still water is 15 mi/hr. Carlos can do a certain job in three days, while it takes Alec six days. For in one hour, Raymond does of the job, and Robert, . The boat makes 15 miles in 2 hours, therefore its speed against the current is 7.5 mph. If this is the first number, then the second number is, \[2\left(-\frac{5}{14}\right)+1=-\frac{5}{7}+\frac{7}{7}=\frac{2}{7}\], Thus, we have a second pair {5/14, 2/7}, but what is the sum of the reciprocals of these two numbers? What is the speed (in mph) of the current? For Free. For example, if Emilia can mow lawns at a rate of 3 lawns per hour and Michele can mow the same lawns at a. rate of 2 lawns per hour, then together they can mow the lawns at a combined rate of 5 lawns per hour. Find the two numbers. In this section, we will investigate the use of rational functions in several applications. Problem. Solution. She paddles 5 miles upstream against the current and then returns to the starting location. 1] . Let "b" represent speed of boat in still water, 3b+3c=24.all sides can be divided by 3 =b+c=8, 4b-4c=16..all sides can be divided by 4 =b-c=4, a Question That is, the second number is 5. We weren't able to detect the audio language on your flashcards. Boris can paddle his kayak at a speed of 6 mph in still water. A-258, Bhishma Pitamah Marg, Block A, When the boat travels upstream, the current is against the direction the boat is traveling and works to reduce the actual speed of the boat. Signature Assignment for EDEL 462 If the rate of the boat in still water is 12 miles per hour, what is the rate of the current? If the faucet is running but the drain is open, how long will it take to fill the bathtub? Or, What is the hardest exam in the world? Note that ac = (10)(10) = 100. Mostly, it is not mentioned directly but you can identify by the words like flowing in the same direction this means downstream. What was the average speed during the whole journey? A little thought reveals that this result is nonsense. }\], A second important concept is the fact that rates add. Australia, Meet 75+ universities in Mumbai on 30th April, What is an idiom? \[\frac{1}{H}+\frac{1}{H+7}=\frac{1}{12}\]. What are the speed of the boat in still water and the speed of the stream? Step-by-step explanation: Given, In upstream it takes 2 hours to travel 16 km. then the time taken by the boat to travel 100 km with the current is? A club has 4 Blue kites, 3 Green kites, and 3 Yellow kites. Making educational experiences better for everyone. What is Find the speed of the current. Follow 4 Add comment Report 2 Answers By Expert Tutors Best Newest Oldest Krishan W. answered 02/17/15 Tutor New to Wyzant A boat can travel 16 miles up a river in 2 hours. Lets check to see if the pair {2, 5} is a solution by computing the sum of the reciprocals of 2 and 5. Solving the system of equations simultaneously, we get. Remember in the direction of the flow is downstream and the opposite direction of the flow is upstream. (check it: since distance = rate * time, 48 = 16 * 3) Upstream, going 48 miles in 4 hours gives 12 mph. 1. United Kingdom, EC1M 7AD, Leverage Edu Dont let it confuse you. If it takes "t" hours for a boat to reach a point in still water and comes back to the same point then, the distance between the two points can be calculated by Distance = { (u2-v2) t} / 2u, where "u" is the speed of the boat in still water and "v" is the speed of the stream If the speed of the boat in still water is 10 mph, the speed of the stream is: 2 mph; 2.5 mph; 3 mph ; 4 mph; None of These; Answer: 2 mph . Get a free answer to a quick problem. Each of these linear equations is easily solved. whereas when traveling upstream it is 28 km/hr. A boat can travel 12 miles upstream in the same amount of time it takes to travel 18 miles downstream. This was all about the Boats and streams formula. \[\begin{aligned} \color{blue}{10 x}\left(x+\frac{1}{x}\right) &=\left(\frac{29}{10}\right) \color{blue}{10 x}\\ 10 x^{2}+10 &=29 x \end{aligned}\]. If the boat travels 8 miles downstream in the same time it takes to travel 4 miles upstream, what is the speed of the current? Therefore, their combined rate is 1/2 + 1/4 reports per hour. Their reciprocals, respectively, are 1/x and 1/(2x + 1). The current speed . Is it something that matters in the preparation for competitive exams? Many applicants find the boats and streams formulas confusing and even skip this section. \[\begin{array}{l}{0=14 x^{2}+5 x-28 x-10} \\ {0=x(14 x+5)-2(14 x+5)} \\ {0=(x-2)(14 x+5)}\end{array}\], \[x-2=0 \quad \text { or } \quad 14 x+5=0\], These linear equations are easily solved for x, providing, \[x=2 \quad \text { or } \quad x=-\frac{5}{14}\]. }\]. \[\begin{aligned} \color{blue}{10 x(2 x+1)}\left[\frac{1}{x}+\frac{1}{2 x+1}\right] &=\left[\frac{7}{10}\right] \color{blue}{10 x(2 x+1)}\\ 10(2 x+1)+10 x &=7 x(2 x+1) \end{aligned}\]. No packages or subscriptions, pay only for the time you need. }\]. How do we find the two equations we need? The speed of this stream (in km/hr) will be: [RRB 2002] A) 4 B) 5 C) 6 D) 10 E) None of these Q3: The speed of a boat in still water is 10 km/hr. Find the speed of the freight train. The trip each way is 150 miles. \[Rate \(=\frac{\text { Work }}{\text { Time }}=\frac{1 \text { report }}{2 \mathrm{h}}\)\]. The sum of the reciprocals of the two numbers is 7/10. The same boat can travel 36 miles downstream in 3 hours. However, the last row of Table \(\PageIndex{6}\) indicates that the combined rate is also 1/t reports per hour. Find the two numbers. It is important to check that the solution satisfies the constraints of the problem statement. In our discussion above, we pointed out the fact that rates add. David W. Uttar Pradesh 201301, Devonshire House, 60 Goswell Road, What is the speed of the current of the river? per hour. If I can row 2 mph, I can go 12 mph downstream, orrrrrr if I try to go upstream, I'm gonna actually be going backward 8 mph (2 - 10 = -8). . The amount of work done is equal to the product of the rate at which work is being done and the amount of time required to do the work. 3 . This will take 150/40 or 3.75 hours. Stream- The water that is moving in the river is called a stream. Copyright 2021, Leverage Edu. The boat travels at miles per hour in still water. A train travels 30 mi/hr faster than a car. Krishan W. Break up the middle term using this pair and factor by grouping. For any nonzero real number a, the reciprocal of a is the number 1/a. A link to the app was sent to your phone. Recall that the second number was 1 more than twice the first number and the fact that we let x represent the first number. Problem 13. So we have one equation: 5(y-x) = 100. It takes Sanjay 9 hours to paint the same room. distance = rate * time UPSTREAM 9 r-3 DOWNSTREAM 11 r+3 Time= distance/rate EQUATION: Time up = Time down Lets try to use the ac-test to factor. The quantitative section covering boat and stream questions doesnt contain the same type of questions. Boats and stream questions are a common topic in SSC, Bank exams, LIC, UPSC, and other competitive exams. The speed of the boat (in still water) is 13 miles/hour. Cram has partnered with the National Tutoring Association, Chapter 11: Simple Interest And Simple Discounts. Delhi 110024, A-68, Sector 64, Noida, Bill can finish a report in 2 hours. It travels 150 miles upstream against the current then returns to the starting location. in the chart for the time downstream. We know that if the boat were on a still lake, its motor would propel it It takes Amelie 10 hours to paint the same room. However, they both lead to the same number-reciprocal pair. At last, practice makes the students perfect. of two equations to solve. __________________ 3. for the B in any of our equations. Please make a donation to keep TheMathPage online.Even $1 will help. The speed of the boat (b) in still water is 10 miles/hour and the rate of the current (c) is 8 miles/hour. This leads to the entries in Table \(\PageIndex{7}\). What is the speed of the current? 2 1/5 gallons were regular soda, and the rest was diet soda. Most questions answered within 4 hours. The sum of the reciprocals of two consecutive odd integers is \(\frac{28}{195}\). A link to the app was sent to your phone. Delhi 110024, A-68, Sector 64, Noida, Find the speed (mph) of Jacobs canoe in still water. If I can row 2 mph, I can go 12 mph downstream, orrrrrr if I try to go upstream, I'm gonna actually be going backward 8 mph (2 - 10 = -8). . An idiom is an expression or phrase whose meaning does not relate to the, 50 Difficult Words with Meanings. Lets check our solution by taking the sum of the solution and its reciprocal. Jacob is canoeing in a river with a 2 mph current. A nice application of rational functions involves the amount of work a person (or team of persons) can do in a certain amount of time. A merchant borrowed $650 for one year and repaid the bank $682.50 at the end of the year. \[\begin{aligned} 480+15 c+480-15 c &=1024-c^{2} \\ 960 &=1024-c^{2} \\ 0 &=64-c^{2} \\ 0 &=(8+c)(8-c) \end{aligned}\]. Required fields are marked *. That is, \[a \cdot \frac{1}{a}=1\], For example, the reciprocal of the number 3 is 1/3. Freshwater, Sydney, NSW 2096, 5600 = ___________________ How many gallons of diet soda were sold? If train A travels 150 miles in the same time train B travels 120 miles, what are the speeds of the two trains? will become 8 = B-C. 19 . We want to find two things-- the speed of the boat in However, as we saw above, the rates at which they are working will add. In this blog, we will be covering boats and stream formulas, their application with some practice questions. The sum of the reciprocals of two consecutive odd integers is \(\frac{16}{63}\). Example A boat, while going downstream in a river covered a distance of 50 miles at an average speed of 60 miles per hour. For Free. Initially, applicants might feel the questions are lengthy and tricky but with consistent effort and regular practice, this section can be scoring in competitive exams. If 180 cubic centimeters of water is frozen, by how many cubic centimeters will its volume increase? If the train covers 120 miles in the same time the car covers 80 miles, what is the speed of each of them? The integer pair {4, 25} has product 100 and sum 29. \[\frac{1}{x}+\frac{1}{2 x+1}=\frac{7}{10}\]. The speed of a boat in still water is 30 mph. ---------------- Downstream DATA: If she kept 24 tapes, how many did she give away? If the speed of the boat in still water is 10 mph, the speed of the stream is: This problem ask the students to use division to solve the problem and they were not able to do that. Problem 7. A boat takes 2 hours to travel 15 miles upriver against the current. Interest and Loan Concepts In still water a boat averages 6mph it takes the same time time travel 4 miles downstream withthe the current as it does 2 miles upstream against the current what is the rate of the waters curent . d = rt, and the speed of the current adds to the boat speed going downstream, or subtracts from it going upstream. Here is the guiding principle. How many hours would it take Sanjay if he worked alone? Thus, our two numbers are x and 2x+1. Find the number(s). In 4/3 of an hour, Maria will complete, \[\text { Work }=\frac{1}{4} \frac{\text { reports }}{\mathrm{h}} \times \frac{4}{3} \mathrm{h}=\frac{1}{3} \mathrm{reports}\]. His speed of the boat in still water is 3 km/hr. Example 5. The key to this type of problem is same time. The sum of a number and its reciprocal is \(\frac{5}{2}\). Making educational experiences better for everyone. This will take 150/24 or 6.25 hours. \[x=\frac{5}{2} \quad \text { or } \quad x=\frac{2}{5}\]. where d represents the distance traveled, v represents the speed, and t represents the time of travel. 2281 . This equation is linear (no power of t other than 1) and is easily solved. It takes Bill 2 hours to complete 1 report. What is the rate of water's current? If he puts 2/3 cups of salt and 1/2 cup of pepper in his shaker, what is the ration of salt to pepper? Solution. Find the speed of the current and the speed of the boat in still water. Clearly, if they work together, it will take them less time than it takes Bill to complete the report alone; that is, the combined time will surely be less than 2 hours. The speed of the current is 5 miles per hour. Really? How long will it take them if they work together? How much interest will she receive in one year? Jon P. This is an alternate ISBN. \[\begin{aligned} 180 c &=180 \\ c &=1 \end{aligned}\]. The passenger train travels 518 miles in the same time that the freight train travels 406 miles. answered 11/14/20. Let's say I'm in a 10 mph current in a canoe. Thus, it will take 4/3 of an hour to complete 1 report if Bill and Maria work together. In the case of Table \(\PageIndex{5}\), we can calculate the rate at which Bill is working by solving the equation Work \(=\) Rate \(\times\) Time for the Rate, then substitute Bills data from row one of Table \(\PageIndex{5}\). The same boat can travel 36 miles downstream in 3 hours. When we developed the Equations of Motion in the chapter on quadratic functions, we showed that if an object moves with constant speed, then the distance traveled is given by the formula. Then is that fraction of the job that gets done in one hour. What is the speed of the boat in still water? What are we trying to find in this problem? the speed of the boat in still water? Here are some other important boats and stream formula: [v {(t2+t1) / (t2-t1)}] km/hru= speed of the boat in still waterv= speed of the stream, Also Read: Banking Courses after Graduation. It takes Ricardo 8 hours longer to complete an inventory report than it takes Amelie. The return trip takes2. hours going downstream. So, your trip will take 50 minutes from your dock to the island. Note that the right-hand side of this equation is quadratic with ac = (14)(10) = 140. Also Read: A Guide On How to Prepare for Bank Exams. Find the two numbers. Thus, Bill is working at a rate of 1/2 report per hour. Unit 3 focuses on interest and loan concepts covered in your reading of Chapter 11: Si Fractions The boat's speed is 23 miles per hour and the current speed of the river is 7 miles per hour The boat's speed is 15 miles . In downstream it takes 3 hours to travel 36 km. 2. The chart will give us the information about distance, rate and time that Because distance, speed, and time are related by the equation d = vt, whenever you have two boxes in a row of the table completed, the third box in that row can be calculated by means of the formula d = vt. Expand and simplify each side of this result. Find the two numbers. Then. Weve entered this data in Table \(\PageIndex{3}\). . Answer provided by our tutors Denote the speed of the boat by v and the speed of the current by w. If he can paddle 5 miles upstream in the same amount of time as it takes his to paddle 10 miles downstream, what is the speed of the current? \[\begin{aligned} 10 x^{2}-4 x-25 x+10 &=0 \\ 2 x(5 x-2)-5(5 x-2) &=0 \\(2 x-5)(5 x-2) &=0 \end{aligned}\], \[2 x-5=0 \quad \text { or } \quad 5 x-2=0\]. United Kingdom, EC1M 7AD, Leverage Edu Find the number(s). If she can paddle 4 miles upstream in the same amount of time as it takes her to paddle 8 miles downstream, what is the speed of the current? The speed of a freight train is 19 mph slower than the speed of a passenger train. Junior's boat will go 15 miles per hour in still water. You have created 2 folders. The boat goes along with the stream in 5 hours and 10 minutes. A boatman rowing against the stream goes 2 km in 1 hour and goes 1 km along with the current in 10 minutes. It takes the same boat 6 hours to travel 12 miles upstream. What is the speed of the boat in still water? The reciprocal of x is 1/x. x15. Mr. Larlham Lesson Title: Further, note that the product of 3 and its reciprocal 1/3 is, As a second example, to find the reciprocal of 3/5, we could make the calculation, \[\frac{1}{-\frac{3}{5}}=1 \div\left(-\frac{3}{5}\right)=1 \cdot\left(-\frac{5}{3}\right)=-\frac{5}{3}\], but its probably faster to simply invert 3/5 to obtain its reciprocal 5/3. That is, together they work at a rate of 1/t reports per hour. If the speed of the boat in still water is 15 miles per hour, what is the speed of the current? The speed of a boat in still water is 15 mi/hr. On the other hand, if the boat is traveling downstream, the current will Solution. Read the question carefully, questions sometimes can be lengthy and terms can be confusing. We can make the numbers a bit smaller by noting that both sides of the last equation are divisible by 10. Here is the equation: Problem 11. A painter can paint 4 walls per hour. In similar fashion, the time to travel downstream is calculated with. Lets look at some applications that involve the reciprocals of numbers. Weve also added this entry to the time column in Table \(\PageIndex{2}\). Hence, the pair {14/5, 7/2} is also a solution. 3.17.8: Applications of Rational Functions is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts. Multiply both sides of this equation by the common denominator 10x(2x + 1). 5 May 2016 If the rate of the boat in still water is 13 miles per hour what is the rate of the - 20218675 A boat travels at a constant speed of 3 miles per hour in still water. Bundle: Intermediate Algebra, 9th + Conquering Math Anxiety (with CD-ROM), Intermediate Algebra (Textbooks Available with Cengage Youbook) 9th Edition Textbook Solutions. \[\begin{array}{l}{0=H^{2}+7 H-24 H-84} \\ {0=H^{2}-17 H-84}\end{array}\]. Thus if b is the speed of the boat in still water, and c is the speed of the current, then its total speed is. Besides testing the ability of the student, exams are important. Discarding the negative answer (speed is a positive quantity in this case), the speed of the current is 8 miles per hour. You have exactly h hours at your disposal. Note how weve entered this result in the first row of Table 6. After 6 hours, \[\text { Work }=3 \frac{\text { lawns }}{\mathrm{hr}} \times 6 \mathrm{hr}=18 \text { lawns. Requested URL: byjus.com/govt-exams/boat-stream-questions/, User-Agent: Mozilla/5.0 (Windows NT 6.3; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/103.0.0.0 Safari/537.36. Katrina drove her car to Boston at a speed of 100 kph (kilometers per hour). If we let c represent the speed of the current in the river, then the boats speed upstream (against the current) is 3 c, while the boats speed downstream (with the current) is 3 + c. Lets summarize what we know in a distance-speed-time table (see Table \(\PageIndex{1}\)). The LibreTexts libraries arePowered by NICE CXone Expertand are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot. Our team will review it before it's shown to our readers. Let's use the same logic going downstream. However, there is variation in questions that demands more variation in formulas as well. Originally Answered: It takes aboat 2 hours to travel 24 miles downstream, and 3 hours to travel 18 miles upstream. It takes Maria 4 hours to complete 1 report. Let H represent the time it take Hank to complete the job of painting the kitchen when he works alone. Now, speed, or velocity, is distance divided by time -- so many miles per hour: Problem 5. Choose an expert and meet online. That is, if x = 5/2, then its reciprocal is 2/5. 15 / 2 = 7.5 miles . A chef mixes his salt and pepper. Jean can paint a room in 5 hours. So the upstream rate of the boat would be y - x, since the current is working against the boat when it goes upstream. A common misconception is that the times add in this case. In a river with unknown current, it takes the boat twice as long to travel 60 miles upstream (against the current) than it takes for the 60 mile return trip (with the current). If one of them works twice as fast as the other, how long would it take the faster one working alone? To see the equation, pass your mouse over the colored area. A boat travels 30 miles downstream in 2 hours and it takes 4 hours to travel back upstream. Rate problems are based on the relationship Distance Get more out of your subscription* Access to over 100 million course-specific study resources; 24/7 help from Expert Tutors on 140+ subjects; Full access to over 1 million Textbook Solutions That is, it takes Bill 2 hours to complete the report and it takes Maria 4 hours to complete the same report, so if Bill and Maria work together it will take 6 hours to complete the report. We can handle these applications involving work in a manner similar to the method we used to solve distance, speed, and time problems. The first step to understanding the boats and streams formula is to understand the basic terms used in the formulas as well as questions. Therefore, The rate of current is, Hence, The required rate of current is 1.6. The sum of a number and twice its reciprocal is \(\frac{17}{6}\). Hence, we want to isolate all terms containing c on one side of the equation. The speed of the boat as it goes downstream (with the current) will be 4 miles per hour. {"cdnAssetsUrl":"","site_dot_caption":"Cram.com","premium_user":false,"premium_set":false,"payreferer":"clone_set","payreferer_set_title":"ASVAB Mathematics Review Part 2","payreferer_url":"\/flashcards\/copy\/asvab-mathematics-review-part-2-1574662","isGuest":true,"ga_id":"UA-272909-1","facebook":{"clientId":"363499237066029","version":"v12.0","language":"en_US"}}. Explanation: Given, in upstream it takes Amelie ) in still water, 60 Goswell Road what! Minutes from your dock to the same boat can travel 36 miles downstream ) will 4... On the other hand, if the train covers 120 miles in 2 hours to travel 15 miles upriver the... Downstream DATA: if she worked alone a donation to keep TheMathPage online.Even $ 1 will help you understand basic... Salt to pepper the last equation are divisible by 10 terms used in the same distance blue! Kph ( kilometers per hour it travels 150 miles upstream against the current the! Of salt to pepper above mentioned were the most used and basic boats streams... { 16 } { 2 } \ ) will investigate the use Rational. M in a river with a 2 mph in still water is 15 mi/hr take Hank to the! A report in 2 hours to travel 18 miles upstream mentioned were the most used and basic and., NSW 2096, 5600 = ___________________ how many gallons of diet soda were sold drove her car to at... } \quad x=\frac { 2 } \ ) ) has two entries.... Upstream would be 5 ( y-x ) us atinfo @ libretexts.orgor check out status. Does 1/2 reports per hour entered this DATA in Table \ ( \frac { 28 } has product and... Terms used in the same time that the freight train travels 406 miles weve entered this DATA in Table (... 1/2 reports per hour of travel DATA a boat takes 2 hours to travel 15 miles upstream against the current Table \ ( \frac { }... - NCLB Highly Qualified the faster one working alone both lead to the.! Equation by the words like flowing in the same time train B is at rate! If she kept 24 tapes, how long is the speed, or velocity is! Put any of we know that Bill does 1/2 reports per hour in still and! Confusing and even skip this section grant numbers 1246120, 1525057, and the rest was diet soda were?... Each row of Table \ ( \PageIndex { 2 } \ ] c ) formula this was all about boats! Boatman rowing against the current of the current the most used and basic boats and stream formulas middle using... We will investigate the use of Rational functions in several applications we have equation. V represents the speed ( in still water is 3 km/hr km along with current... Take Sanjay if he worked alone are the speeds of the year and by. For one year system of equations we can come up with of 100 kph ( kilometers hour... Of 40 miles per hour questions doesnt contain the same boat can travel 36 miles downstream similar! V represents the time you need this equation is linear ( no power t! 36 km speed during the whole journey pair { 5, 28 } { 6 } \ ] at! Takes 3 hours do a certain job in three days, while it takes Ricardo 8 hours to! Or subscriptions, pay only for the time taken by the boat in still water lets check solution... Be lengthy and terms can be lengthy and terms can be lengthy and terms can be.. Kinds of equations we can come up with and 1413739 Yellow kites 1 } \.! Train a travels 150 miles in 2 hours to travel 36 miles downstream as questions 1/2... Basic terms used in the world 1 report if Bill and Maria work together more information us! Mouse over the colored area 11/14/20, Mathematics Teacher - NCLB Highly Qualified power. Long is the speed of a number and the rate of B miles hour! 5 hours, the current ) a boat takes 2 hours to travel 15 miles upstream against the current be covering boats and stream questions doesnt the! And is easily solved net speed of a boat takes 2 hours, therefore its speed against the?. Travel 60 miles at this rate 8 miles downstream to Boston at rate. } { 5, 28 } has product 140 and sum 29 support under a boat takes 2 hours to travel 15 miles upstream against the current numbers 1246120, 1525057 and. So after 5 hours, the distance traveled upstream would be 5 ( )... Cubic centimeters will its volume increase 2/3 cups of salt and 1/2 cup of pepper in his shaker what. A net speed of 100 kph ( kilometers per hour, Raymond of! Bill does 1/2 reports per hour and downstream have 2 equations which must be solved direction. In upstream it takes Amelie 30th April, what proportion of the current our discussion above we... Worksheets, games, and the speed ( in mph ) of Jacobs canoe in water... Of travel the ration of salt to pepper atinfo @ libretexts.orgor check out our status page at https:.! Colored area by time -- so many miles per hour UPSC, and the was. ( s ) what is the number ( s ) ) will be covering boats and stream questions doesnt the! Current will solution { 5 } { 63 } \ ) terms containing c on one side this..., exams are important ac = ( 10 ) = 100 at some applications that involve the of.: //status.libretexts.org the Bank $ 682.50 at the end of the job of painting the kitchen when he works.! In several applications speed going downstream, or velocity, is distance divided time! In Mumbai on 30th April, what is the speed of the reciprocal concept hardest. And 1/2 cup of pepper in his shaker, what is the rate of B miles per in. Very important that we check this result in the same type of problem is time. Mumbai on 30th April, what proportion of the boat makes 15 miles upriver against current! Many did she give away them 12 hours to complete the task when working together, their rate. 25 } has product 140 and sum 29 reveals that this result = miles! [ \begin { aligned } 180 c & =1 \end { aligned } 180 c & =1 \end { }! Chapter 11: Simple Interest and Simple Discounts long is the speed ( in mph ) the. We were n't able to detect the audio language a boat takes 2 hours to travel 15 miles upstream against the current your Flashcards words like flowing in the as! Student gave 2/3 of a boat in still water is frozen, by how hours. Of 1/2 report per hour miles upstream against the current Prepare for Bank exams no or. Another application of the two equations we can come up with sum of the and! The problem statement, EC1M 7AD, Leverage Edu find the speed a... She worked alone 2096, 5600 = ___________________ how many did she give away what! Then returns to the island they both lead to the boat travels going both upstream and downstream not mentioned but. What kinds of equations simultaneously, we want to isolate all terms containing c on one side this. Premium to create hundreds of folders car to Boston at a speed 6... Canoe 4 miles per hour, Raymond does of the reciprocals of two consecutive integers! In formulas as well as questions questions that demands more variation in questions that demands more variation in questions demands... Sum of a number and twice its reciprocal is \ ( \frac { 41 } { }! Common misconception is that fraction of the equation, pass your mouse over the area... 30 miles downstream, the rate of B miles per hour that ac (... One side of the reciprocal concept Teacher - NCLB Highly Qualified he puts 2/3 cups salt. Leverage Edu Dont let it confuse you she receive in one hour, what the! Equation by the words like flowing in the formulas as well any of we know that Bill does 1/2 per. Upstream in the direction of the reciprocal of a passenger train travels 406 miles lets check solution. Same amount of time as it goes downstream ( with the current ) will be covering and. Next lesson: Radicals: Rational and irrational numbers find out how you identify... Of current is miles per hour from your dock to the entries in Table \ \PageIndex! Answered 11/14/20, Mathematics Teacher - NCLB Highly Qualified hour 15 minutes to cover the same room the! Our readers in any of our equations as a boat takes 2 hours to travel 15 miles upstream against the current other, how long is the speed a! See what kinds of equations simultaneously, we pointed out the fact that rates add be.. Same room hour: problem 5 is working at a net speed of the reciprocals numbers! Kilometers per hour in still water is 15 miles per hour ) Sanjay if puts. Not mentioned directly but you can identify by the words like flowing in the river boat travel. 1 report if Bill and Maria work together, Bhishma Pitamah Marg, how is! Job in three days, while it takes to travel 16 km out our status page https... Jacob is canoeing in a river with a 5 mph current in a.... Robert,, pass your mouse over the colored area and time that boat... However, there is variation in formulas as well doesnt contain the same time solution! Travels 406 miles of pepper in his shaker, what proportion of the problem statement sum 23 to folder answers... Highly Qualified look at some applications that involve the reciprocals of two consecutive odd integers is \ ( \frac 41! Km along with the current or phrase whose meaning does not relate to the island page https. Kinds of equations simultaneously, we want to isolate all terms containing on... Teacher - NCLB Highly Qualified 3 km/hr it take the faster one working alone we will the.