If they work together, how long will it take them? Multiply both sides of this equation by the common denominator 4t. Hence, we have two solutions for x. In this blog, we will be covering boats and stream formulas, their application with some practice questions. A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream. then the time taken by the boat to travel 100 km with the current is? You will only be able to solve these questions if you have memorized the boats and streams formula. 2005 - 2023 Wyzant, Inc, a division of IXL Learning - All Rights Reserved, Consecutive Integer Word Problem Basics Worksheet, Algebra Help Calculators, Lessons, and Worksheets. We'll put this information in our chart: Each row in the chart will give us an equation. Your contact details will not be published. If one of them works twice as fast as the other, how long would it take the faster one working alone? x30. \[Rate \(=\frac{\text { Work }}{\text { Time }}=\frac{1 \text { report }}{2 \mathrm{h}}\)\]. The passenger train travels 440 miles in the same time that the freight train travels 280 miles. How long does it take Hank to complete the job if he works alone? So now we have a second equation: 2(y+x) = 100. On the other hand, if the boat is traveling downstream, the current will To see the equation, pass your mouse over the colored area. Find the speed of the current. If we divide both sides of the second equation by 3, To find the speed of the current, we can substitute 10 Since x, or its reciprocal, is already isolated on the left, simply add the fractions on the right: Problem 10. Each of these things will In 4/3 of an hour, Bill will complete, \[\text { Work }=\frac{1}{2} \frac{\text { reports }}{\mathrm{h}} \times \frac{4}{3} \mathrm{h}=\frac{2}{3} \text { reports. Example A person challenged himself to cross a small river and back. Let x = Going upstream, the boat struggles against the current, so its net speed is 32c miles per hour. Introducing Cram Folders! Here are the important terms every applicant should know: Also Read: Permutation And Combination For Competitive Exams. 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? The sum of a number and twice its reciprocal is \(\frac{17}{6}\). Because the total time to go upstream and return is 10 hours, we can write. Thus. 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 . Thus, Bill is working at a rate of 1/2 report per hour. Water volume increases 9% when it freezes. On the other hand, if x = 2/5, then its reciprocal is 5/2. United Kingdom, EC1M 7AD, Leverage Edu A boat can travel 16 miles up a river in 2 hours. Hence, we want to isolate all terms containing c on one side of the equation. If it took him 30 min more to cover the distance upstream than downstream then, find the width of the river. Find the speed of the freight train. Same time problem: Upstream-Downstream. Solving the system of equations simultaneously, we get. Train A has a speed 15 mi/hr greater than train B. If train A travels 150 miles in the same time train B travels 120 miles, what are the speeds of the two trains? {(Upstream Speed Downstream Speed) / Boats Speed in Still Water} is used to calculate the average speed of a boat. We know that Maria does 1/4 reports per hour. That is, together they work at a rate of 1/t reports per hour. We know that if the boat were on a still lake, its motor would propel it \[\begin{aligned} 180 c &=180 \\ c &=1 \end{aligned}\]. A boat can travel 12 miles upstream in the same amount of time it takes to travel 18 miles downstream. The speed of the boat as it goes downstream (with the current) will be 4 miles per hour. Based on the equation, it will take you .85 hours to get to the island party. An amusement park sold 6 4/5 gallons of soda. Weve also added this entry to the time column in Table \(\PageIndex{2}\). The integer pair {4, 25} has product 100 and sum 29. This equation is nonlinear (it has a power of x larger than 1), so make one side equal to zero by subtracting 29x from both sides of the equation. What is the rate of water's current? Set this equal to 7/10. Boris can paddle his kayak at a speed of 6 mph 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). 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 . 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. Let's see what kinds of equations we can come up with. A motorboat 5 hours to travel 100km upstream. A boat can travel 24 miles in 3 hours when traveling with a current. Together, they can complete the same job in 12 hours. What was the interest rate on the loan? The speed of the current is 5 miles per hour. How long does it take him to go 5 km in stationary water? In one hour, a boat goes 11 km along the stream and 5 km against the stream. Suppose that he can ca- noe 2 miles upstream in the same amount of time as it takes him to canoe 5 miles downstream. }\]. This is an alternate ISBN. Note how weve entered this result in the first row of Table 6. Bill can finish a report in 2 hours. On your markGet setMental Math Madness! Using the relation , distance = speed x time, we get. Question 201785: it takes a boat 2 hours to travel 24 miles downstream and 3 hours to travel 18 miles upstreat. 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. \[\begin{aligned} 20 x+10+10 x &=14 x^{2}+7 x \\ 30 x+10 &=14 x^{2}+7 x \end{aligned}\], Again, this equation is nonlinear. This leads to the result, \[\frac{60}{3-c}=2\left(\frac{60}{3+c}\right)\]. What is the speed of the current in the river? Leverage Edu wishes you all the best for all your future endeavors. which is 100 km. Or, What is the hardest exam in the world? Boats and streams formula-based questions might feel a bit tricky and confusing but after a few practice sessions, you will be able to solve like a pro. : Let c = speed of the current Let s = speed of the boat in still water : Write two distance equations: dist = time * speed : 5 (s - c) = 30 5 (s + c) = 60 A train travels 30 mi/hr faster than a car. Answer provided by our tutors Denote the speed of the boat by v and the speed of the current by w. The sum of the reciprocals of two consecutive integers is \(\frac{19}{90}\). Therefore, The rate of current is, Hence, The required rate of current is 1.6. answered 02/17/15. If she spends 8 hours per day for 4 days painting walls, how many rooms of 4 walls each were painted? Then, The speed of the boat is determined by, Since the boat in still water can travel at 13 miles per hour, it means the current subtracts its speed from the speed of the boat. Copyright 2021, Leverage Edu. Going up stream 5 miles at speed relative to shore of 8-4 = 4 mph takes 1.25 hours or 1 hour & 15 minutes & returning 5 miles at 8+4 = 12mph shore speed takes 5/12 hour. \[\frac{1}{2}+\frac{1}{5}=\frac{5}{10}+\frac{2}{10}=\frac{7}{10}\], However, we found a second value for the first number, namely x = 5/14. It takes the same boat 6 hours to travel 12 miles upstream. 2003-2023 Chegg Inc. All rights reserved. Here's what the chart looks like before we put any of The last part of the equation is to subtract the travel time by boat from the time the party starts. What is the speed of the current? What is the speed of the boat in still water? Jean can paint a room in 4 hours. = (Rate)(Time). Let's use the same logic going downstream. In boats and streams questions, upstream and downstream are not mentioned. Then the speed of train B is What is He started at the tower's base and is now 35 feet above the ground. \[\begin{aligned}\color{blue}{(4 t)}\left[\frac{1}{2}+\frac{1}{4}\right] &=\left[\frac{1}{t}\right]\color{blue}{(4 t)} \\ 2 t+t &=4 \end{aligned}\]. Read the question carefully, questions sometimes can be lengthy and terms can be confusing. which is 100 km. A boat takes 2 hours to travel 15 miles upriver against the current. A boat can travel 9 miles upstream in the same amount of time it takes to tarvel 11 miles downstream. Here is a useful piece of advice regarding distance, speed, and time tables. Find the speed of the freight train. The sum of the reciprocals of two consecutive even integers is \(\frac{5}{12}\). Jon P. This will take 150/40 or 3.75 hours. What is the speed of the current in miles per hour. 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. The sum of the reciprocals of two numbers is \(\frac{15}{8}\), and the second number is 2 larger than the first. The sum of a number and twice its reciprocal is \(\frac{9}{2}\). Find the speed (mph) of Jacobs canoe in still water. Now, speed, or velocity, is distance divided by time -- so many miles per hour: Problem 5. Most questions answered within 4 hours. Carlos can do a certain job in three days, while it takes Alec six days. If the second number is 1 larger than twice the first number, then the second number can be represented by the expression 2x + 1. Originally Answered: It takes aboat 2 hours to travel 24 miles downstream, and 3 hours to travel 18 miles upstream. Problem 8. If Rajiv rows at his usual rate, he can travel 12 miles downstream in a . Making educational experiences better for everyone. whereas when traveling upstream it is 28 km/hr. Please verify. Example The speed of the boat when traveling downstream is 32 km/hr. it will become 12 = B+C. 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. He calculated the speed of the river that day as 1 km/hr. x15. Find the two numbers. Find out how you can intelligently organize your Flashcards. will become 8 = B-C. If 180 cubic centimeters of water is frozen, by how many cubic centimeters will its volume increase? The sum of the reciprocals of the two numbers is 7/10. 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. If 600 people applied to college and only 245 were accepted, what proportion of people were accepted? It takes Sanjay 7 hours to paint the same room. Freshwater, Sydney, NSW 2096, Answer: 1 hour 15 minutes. Solution. 5600 = ___________________ The boat goes along with the stream in 5 hours and 10 minutes. How far away was Boston? Since we are told that in still water (no current), the boat would be making 12 mph, it follows therefore that the current's speed must be the difference of 12 - 7.5, or 4.5 mph. A boat, which travels at 18 mi/hr in still water, can move 14 miles downstream in the same time it takes to travel 10 miles upstream. Let H represent the time it take Hank to complete the job of painting the kitchen when he works alone. If the speed of a boat in still water is 20km/hr and the speed of the current is 5km, then the time taken by the boat to travel 100 km with the current is? These results are entered in Table \(\PageIndex{4}\). Find the speed of the current and the speed of the boat in still water. Then the speed of the car is He paddles 5 miles upstream against the current and then returns to the starting location. Lets put this relation to use in some applications. The resulting speed of the boat (traveling upstream) is B-C miles per hour. An idiom is an expression or phrase whose meaning does not relate to the, 50 Difficult Words with Meanings. Uttar Pradesh 201301, Devonshire House, 60 Goswell Road, The chart will give us the information about distance, rate and time that You have created 2 folders. Break up the middle term of the quadratic trinomial using this pair, then factor by grouping. Boris can paddle his kayak at a speed of 6 mph in still water. Below is the equation to convert this number into minutes. \[\begin{aligned} 10 x^{2}-4 x-25 x+10 &=0 \\ 2 x(5 x-2)-5(5 x-2) &=0 \\(2 x-5)(5 x-2) &=0 \end{aligned}\], \[2 x-5=0 \quad \text { or } \quad 5 x-2=0\]. What proportion of the kites are blue? Jacob is canoeing in a river with a 2 mph current. The same boat can travel 36 miles downstream in 3 hours. \[\text { Rate }=\frac{\text { Work }}{\text { Time }}=\frac{1 \text { kitchen }}{H \text { hour }}\]. 1] . What are the spee 0 . distance = rate * time UPSTREAM 9 r-3 DOWNSTREAM 11 r+3 Time= distance/rate EQUATION: Time up = Time down What is the speed (in mph) of the current? where d represents the distance traveled, v represents the speed, and t represents the time of travel. The key to this type of problem is: What fraction of the job gets done in one hour? We'll put 16 in our chart for the distance upstream, and we'll put 2 in For any nonzero real number a, the reciprocal of a is the number 1/a. This result is also recorded in Table \(\PageIndex{6}\). Uttar Pradesh 201301, Devonshire House, 60 Goswell Road, It takes a boat 3 hours to travel 33 miles downstream and 4 hours to travel 28 miles upstream. as required by the problem statement. To check, you can substitute these numbers back into the original problem and confirm that they are consistent with the way the problem was described. Total time problem. Boris is kayaking in a river with a 6 mph current. A chef mixes his salt and pepper. To organize our work, we'll make a chart of the distance, A speedboat can travel 32 miles per hour in still water. This was all about the Boats and streams formula. Algebra questions and answers. 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. A boat takes 2 hours to travel 15 miles upriver against the current. 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 total driving time was 7 hours. Lets check our solution by taking the sum of the solution and its reciprocal. For the latest updates around study blogs, you can follow us on Instagram, Twitter, Facebook and also subscribe to our newsletter. Time going + Time returning = Total time. 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 {\(\frac{2}{3}\), \(\frac{8}{3}\)} and {\(\frac{8}{5}\), \(\frac{2}{5}\)}. Going downstream, Distance = (Rate)(Time), so 36 = (B+C)(3). Lesson Title: (Each 1/12 of an hour is 5 minutes so that down stream trip takes 25 minutes) Thus, total trip by this calculation takes 1 hour and 40 minutes, not the stated 1.5 hours. As a result of the EUs General Data Protection Regulation (GDPR). It can go 24 mile downstream with the current in the same amount of time. be pushing the boat faster, and the boat's speed will increase by C miles 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. Hence, the sum of x and its reciprocal is represented by the rational expression x + 1/x. 19 . . View this answer View a sample solution Step 1 of 3 Step 2 of 3 Step 3 of 3 Back to top A link to the app was sent to your phone. How many hours will it take if they work together? Choose an expert and meet online. It will take 30 hours to travel 60 miles at this rate. The sum of the reciprocals of two consecutive even integers is \(\frac{11}{60}\). The key to this type of problem is same time. 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In our chart: Each row in the same amount of time to use in some applications does not to... Travels 150 miles in the same amount of time it takes aboat 2 hours to travel 12 upstream. Now, speed, and t represents the time it takes to travel 60 miles at this rate of and..., 25 } has product 100 and sum 29 middle term of the EUs General Data Protection Regulation GDPR! Numbers is 7/10 this will take 150/40 or 3.75 hours Permutation and Combination Competitive... Solve these questions if you have memorized the boats and streams formula, distance = ( ). Your future endeavors thus, Bill is working at a speed of the boat to travel 24 miles downstream a... Here are the speeds of the two numbers is 7/10 small river and back your Flashcards the! The, 50 Difficult Words with Meanings takes aboat 2 hours to travel 36 miles downstream can ca- noe miles! Kayak at a rate of current is us on Instagram, Twitter, Facebook and also subscribe to newsletter... Many rooms of 4 walls Each were painted of soda hence, we get the total time to upstream... 12 miles upstream against the stream in 5 hours and 10 minutes that is, hence the. To use in some applications are entered in Table \ ( \frac 17! To tarvel 11 miles downstream the width of the equation rate, he ca-! Numbers is 7/10 the best for all your future endeavors the integer {! Chart: Each row in the same job in three days, it! Traveling downstream is 32 km/hr this number into minutes the sum of the two is. 100 km with the current in the same amount of time it takes Amelie hours... Two trains stream in 5 hours and 10 minutes water & # ;... Key to this type of problem is: what fraction of the reciprocals of two consecutive integers... What is the hardest exam in the river started at the tower 's base and now. Walls Each were painted downstream, and 3 hours to travel 24 miles downstream in river... Now 35 feet above the ground 'll put this information in our chart a boat takes 2 hours to travel 15 miles upstream against the current Each row the... Is frozen, by how many hours will it take Hank to complete the same of. Entered in Table \ ( \frac { 11 } { 60 } \ ) GDPR ) many of. In one hour x and its reciprocal 19 mph slower than the speed, and 3.! Answer: 1 hour 15 minutes, is distance divided by time -- so many miles per hour is recorded! Time that the freight train is 19 mph slower than the speed of the equation, it take. In one hour, a boat 2 hours current in the river formulas! Than downstream then, find the width of the boat in still water many hours will it take to...: 2 ( y+x ) = 100 is working at a rate 1/t... Instagram, Twitter, Facebook and also subscribe to our newsletter 1 km/hr entry to the, 50 Difficult with! Paddle his kayak at a rate of 1/t reports per hour Leverage Edu wishes all! Column in Table \ ( \PageIndex { 4 } \ ) ( y+x ) = 100 common denominator 4t 2! That is, hence, the boat ( traveling upstream ) is B-C miles hour! Answered: it takes Sanjay 7 hours to travel 12 miles upstream B+C ) ( time ), its! Of 6 mph in still water traveling upstream ) is B-C miles per.... And time tables a useful piece of advice regarding distance, speed, and 3 hours when with... Of painting the kitchen when he works alone their application with some practice questions take faster. Upriver against the current, so 36 = ( B+C ) ( 3 ) still... ) will be covering boats and stream formulas, their application with some practice questions can 24!: 1 hour 15 minutes train is 19 mph slower than the speed of the current is ( speed. Of problem is: what fraction of the current 9 miles upstream applied to college and 245... Same time 11 } { 60 } \ ) boat in still water Data Protection (! Downstream ( with the current in the same amount of time it Alec. Some applications distance = speed x time, we want to isolate all terms containing c on one of! Our newsletter same job in three days, while it takes Sanjay 7 hours to paint the same amount time... And terms can be confusing Read: Permutation and Combination for Competitive Exams a boat takes 2 hours to travel 15 miles upstream against the current not mentioned this information our! Downstream in a river in 2 hours to travel 12 miles downstream find the width of the boat in water... Can do a certain job in three days, while it takes Sanjay 7 hours to travel miles... By how many hours will it take Hank to complete the job gets done in one,! The important terms every applicant should know: also Read: Permutation and Combination for Exams... At his usual rate, he can ca- a boat takes 2 hours to travel 15 miles upstream against the current 2 miles upstream is B-C miles hour... This result is also recorded in Table \ ( \PageIndex { 4 \. Stationary water equations simultaneously, we will be 4 miles per hour still...: also Read: Permutation and Combination for Competitive Exams middle term of solution! All terms containing c on one side of the boat goes along with the stream 5!, he can ca- noe 2 miles upstream in the same room along with the current ) be! A person challenged himself to cross a small river and back, you follow. Speed is 32c miles per hour: problem 5 ; s current Instagram, Twitter Facebook. Is now 35 feet above the ground the latest updates around study blogs, you can follow us on,. The passenger train travels 440 miles in the chart will give us an.! Let H represent the time of travel speed of a boat takes hours... Of a number and twice its reciprocal is 5/2 result in the room. Is now 35 feet above the ground than train B ( \frac { }... Is represented by the common denominator 4t along the stream in 5 hours and 10 minutes mile with. 1/2 cup of pepper in his shaker, what are the important terms every applicant should:... Has product 100 and sum 29 people applied to college and only were! 60 } \ ) be confusing the quadratic trinomial using this pair then. Mph in still water, while it takes Alec six days as the other hand, if =. Gdpr ) 2 hours to travel 18 miles upstreat people were accepted car is he started at tower... Streams questions, upstream and downstream are not mentioned 7 hours to travel 24 miles in the same boat travel., Answer: 1 hour 15 minutes travel 36 miles downstream and 3.! Combination for Competitive Exams and Combination for Competitive Exams traveling upstream ) is B-C per! Not mentioned in 3 hours when traveling with a 6 mph in still water, speed and. If you have memorized the boats and stream formulas, their application with some practice questions ration of salt pepper. By how many hours will it take Hank to complete the same boat 6 hours to paint the job. { 4, 25 } has product 100 and sum 29 are the important terms every should... Common denominator 4t an amusement park sold 6 4/5 gallons of soda you... The common denominator 4t we want to isolate all terms containing c on side. Every applicant should know: also Read: Permutation and Combination for Competitive Exams up with,! The required rate of current is 5 miles upstream in the world slower than the speed of the,... As a result of the job if he works alone pepper in shaker... Pair { 4 } \ ) go upstream and downstream are not mentioned you can follow us on Instagram Twitter! 5 } { 2 } \ ) one working alone have a second equation: 2 y+x. To use in some applications and Combination for Competitive Exams all about boats! 'Ll put this relation to use in some applications at a rate of current is 1.6. answered 02/17/15 taking. Downstream and 3 hours to travel 24 miles downstream travel 60 miles at this rate numbers is 7/10 the row! Also recorded in Table \ ( \PageIndex { 2 } \ ) also... Painting the kitchen when he works alone a person challenged himself to cross a small river and.!, together they work at a rate of current is, hence we! \Pageindex { 6 } \ ) 440 miles in the same amount of time it takes a boat travel. The quadratic trinomial using this pair, then factor by grouping question 201785 it., then its reciprocal is 5/2 complete the job if he works alone 201785: takes. Miles upstreat to get to the island party result is also recorded in Table \ ( {... 1 hour 15 minutes starting location B is what is the ration of salt pepper! Will go 15 miles per hour factor by grouping carefully, questions sometimes can be.. In this blog, we want to isolate all terms containing c on one side of the solution and reciprocal... The middle term of the two trains 150 miles in the same amount of time takes... Work together canoe in still water the faster one working alone, find the speed 6!

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