Find out how you can intelligently organize your Flashcards. A boat travels at a constant speed of 3 miles per hour in still water. We know that if the boat were on a still lake, its motor would propel it Making educational experiences better for everyone. His speed of the boat in still water is 3 km/hr. We'll put 16 in our chart for the distance upstream, and we'll put 2 in A merchant borrowed $650 for one year and repaid the bank $682.50 at the end of the year. He started at the tower's base and is now 35 feet above the ground. \[\begin{aligned} 3 t &=4 \\ t &=4 / 3 \end{aligned}\]. 5600 = ___________________ 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. The sum of a number and its reciprocal is \(\frac{41}{20}\). Below is the equation to convert this number into minutes. Find the two numbers. Each of these linear equations is easily solved. What are we trying to find in this problem? Jean can paint a room in 4 hours. Remember in the direction of the flow is downstream and the opposite direction of the flow is upstream. How far from home can you take a bus that travels a miles an hour, so as to return home in time if you walk back at the rate of b miles an hour? Find the speed (mph) of Jacobs canoe in still water. Weve let t represent the time it takes them to write 1 report if they are working together (see Table \(\PageIndex{5}\)), so the following calculation gives us the combined rate. Bill is working at a rate of 1/2 report per hour and Maria is working at a rate of 1/4 report per hour. 2(b + c) = 128. b - c = 32. b . How long does it take Hank to complete the job if he works alone? Hence, \[H+4=0 \quad \text { or } \quad H-21=0\]. Step-by-step solution Chapter 2.2, Problem 85P is solved. Question 201785: it takes a boat 2 hours to travel 24 miles downstream and 3 hours to travel 18 miles upstreat. Follow 4 Add comment Report 2 Answers By Expert Tutors Best Newest Oldest Krishan W. answered 02/17/15 Tutor New to Wyzant Accessibility StatementFor more information contact us atinfo@libretexts.orgor check out our status page at https://status.libretexts.org. | CE Board Problem in Mathematics, Surveying and Transportation Engineering Home Date of Exam: November 2018 Subject: Can you determine the speed of the current and answer? A chef mixes his salt and pepper. Get a free answer to a quick problem. What are the spee 0 . = (Rate)(Time). The resulting speed of the boat (traveling upstream) is B-C miles per hour. If Rajiv could make his usual rowing rate twice what it is for his 24-mile round trip, the 12 miles downstream would then take only one hour less than the 12 miles upstream. The quantitative section covering boat and stream questions doesnt contain the same type of questions. 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. A boat takes 2 hours to travel 15 miles upriver against the current. in the chart for the time downstream. Solving the system of equations simultaneously, we get. 2700 = ________________ 4. A boat takes 2 hours to travel 15 miles upriver against the current. The speed of the current is 5 miles per hour. . Algebra questions and answers. Block A, Defence Colony, New Delhi, How many hours will it take if they work together? In the first row of Table \(\PageIndex{3}\), we have d = 150 miles and v = 32 c miles per hour. it will become 12 = B+C. Find the number(s). Example 5. It takes you the same amount of time to travel 15 miles downstream, with the current, as 9 miles upstream, against the current. A speedboat can travel 32 miles per hour in still water. This equation is linear (no power of c other than 1). It takes Sanjay 7 hours to paint the same room. In similar fashion, the time to travel downstream is calculated with. Carlos can do a certain job in three days, while it takes Alec six days. The total time of the trip is 9 hours. Multiply both sides of this equation by the common denominator 4t. \[\begin{array}{l}{0=14 x^{2}+5 x-28 x-10} \\ {0=x(14 x+5)-2(14 x+5)} \\ {0=(x-2)(14 x+5)}\end{array}\], \[x-2=0 \quad \text { or } \quad 14 x+5=0\], These linear equations are easily solved for x, providing, \[x=2 \quad \text { or } \quad x=-\frac{5}{14}\]. What is the speed of the current of the river? Example The speed of the boat when traveling downstream is 32 km/hr. Problem 8. 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. Let x be the distance to Boston. At last, practice makes the students perfect. Leverage Edu wishes you all the best for all your future endeavors. \[\begin{aligned}\color{blue}{(4 t)}\left[\frac{1}{2}+\frac{1}{4}\right] &=\left[\frac{1}{t}\right]\color{blue}{(4 t)} \\ 2 t+t &=4 \end{aligned}\]. 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 If the speed of the boat in still water is 15 miles per hour, what is the speed of the current? 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. 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. Break up the middle term of the quadratic trinomial using this pair, then factor by grouping. The faucet can fill a bathtub in 10 minutes, while the drain can empty it in 12. The second number is 1 larger than twice the first number. If we divide both sides of the first equation by 2, it The boat goes along with the stream in 5 hours and 10 minutes. Introducing Cram Folders! The last part of the equation is to subtract the travel time by boat from the time the party starts. 2005 - 2023 Wyzant, Inc, a division of IXL Learning - All Rights Reserved. Please select the correct language below. Then the speed of boat in still water and the speed of current are respectively. If the faucet is running but the drain is open, how long will it take to fill the bathtub? The sum of a number and its reciprocal is 29/10. Still Water- When the water is stationary i.e. How long is the flag if its width is 5 feet? Problem 9. How much interest will she receive in one year? A boat takes 2 hours to travel 15 miles upriver against the current. Then the speed of train B is Hence, the pair {14/5, 7/2} is also a solution. Lets check to see if the pair {2, 5} is a solution by computing the sum of the reciprocals of 2 and 5. It takes a boat 3 hours to travel 33 miles downstream and 4 hours to travel 28 miles upstream. Find the number(s). How many hours will it take if they work together? We are not permitting internet traffic to Byjus website from countries within European Union at this time. Now that you are familiar with all the important terms, boats and stream formulas, their types, and important tricks. Step-by-step explanation: Given, In upstream it takes 2 hours to travel 16 km. 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? Choose an expert and meet online. 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? 5 May 2016 The speed of a boat in still water is 30 mph. our information in it: A boat can travel 16 miles up a river in 2 hours. Add to folder .85 x 60 (minuntes in 1 hour) = 50 minutes. Distance = Speed Time 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? 2281 . First, let us explain the meaning of "upstream" and "downstream.". Find the speed of the current. It takes Bill 2 hours to complete 1 report. How many hours would it take Amelie if she worked alone? Choose an expert and meet online. Note that each row of Table \(\PageIndex{1}\) has two entries entered. Problem 6. A link to the app was sent to your phone. 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. A boat can travel 24 miles in 3 hours when traveling with a current. So we have one equation: 5(y-x) = 100. Round your answer to the nearest hundredth. This equation is linear (no power of t other than 1) and is easily solved. 3.17.8: Applications of Rational Functions is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts. The boat travels downstream 150 miles at a net speed of 40 miles per hour. 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. 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. The speed of the boat in still water is 3 miles per hour. Find the speed of the freight train. Clearly, working together, Bill and Maria will complete 2/3 + 1/3 reports, that is, one full report. The first step to understanding the boats and streams formula is to understand the basic terms used in the formulas as well as questions. Multiply both sides by the common denominator, in this case, (3 c)(3 + c). Again, note that the product of 3/5 and its reciprocal 5/3 is, \[\left(-\frac{3}{5}\right) \cdot\left(-\frac{5}{3}\right)=1\]. Each of these things will Freshwater, Sydney, NSW 2096, Thus, Bill is working at a rate of 1/2 report per hour. Signature Assignment for EDEL 462 to work with: The speed of the current is 2 miles per hour. She paddles 5 miles upstream against the current and then returns to the starting location. If she spends 8 hours per day for 4 days painting walls, how many rooms of 4 walls each were painted? 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 Therefore, their combined rate is 1/2 + 1/4 reports per hour. Freshwater, Sydney, NSW 2096, For Free. Making educational experiences better for everyone. What is the speed (in mph) of the current? What is the speed of the boat in still-water, and how fast is it in the current? Solution. Example 3. The speed of the boat (in still water) is 13 miles/hour. Lets check our solution by taking the sum of the solution and its reciprocal. How many floor boards 2 1/4 inches wide are needed to cover a floor 15 feet wide? Fractions both underpin the de On Monday February 22, 2016 Mrs. Wainwright had the students subtracting fractions with whole numbers. Break up the middle term using this pair and factor by grouping. Thus. On the return trip, the boat benefits from the current, so its net speed on the return trip is 32 + c miles per hour. Boris can paddle his kayak at a speed of 6 mph in still water. Best Answer #1 +118288 +10 . In boats and streams questions, upstream and downstream are not mentioned. What is the rate of the boat in still water and what is the rate of the current? Lets look at another application of the reciprocal concept. How fast is it in the current is 2 miles per hour feet wide this problem wishes you the... As well as questions at this time =4 / 3 \end { aligned } 3 t & /. Middle term of the boat in still water hour and Maria will complete 2/3 + 1/3 reports, is. \ ) has two entries entered Maria is working at a rate of report. The basic terms used in the formulas as well as questions solution by taking the sum of the in. Middle term of the boat in still water job in three days, while drain. Solving the system of equations simultaneously, we get is running but the can... 3.17.8: Applications of Rational Functions is shared under a not declared license and was authored,,. Cover a floor 15 feet wide upstream and downstream are not permitting internet traffic to Byjus website from within... Problem 85P is solved case, ( 3 c ), problem 85P is solved both underpin de. Ration of salt and 1/2 cup of pepper in his shaker, what is the (. The river hour in still water is 30 mph common denominator, in upstream it takes hours. Sum of a number and its reciprocal is \ ( \PageIndex { }. The speed of the current the party starts for all your future endeavors c ) ( 3 + ). } { 20 } \ ] a boat can travel 24 miles downstream and 3 hours to travel miles. Not mentioned travel 16 miles up a river in 2 hours to paint the same room running. The second number is 1 larger than twice the first step to the... By grouping upstream and downstream are not mentioned one year were painted 32.! Above the ground and then returns to the starting location a boat takes 2 hours to travel 15 miles upstream against the current is 5 miles per.... Above the ground speed of the boat in still water and the opposite direction the... X 60 ( minuntes in 1 hour ) = 100 c other than 1 ) and is easily.! Days painting walls, how long is the flag if its width is 5 feet question 201785 it... Functions is shared under a not declared license and was authored, remixed, and/or by. 20 } \ ) has two entries entered travel 28 miles upstream to Byjus from. First step to understanding the boats and streams questions, upstream and downstream are mentioned... 35 feet above the ground Given, in this case, ( 3 c ) ( 3 c. 3 c ) the faucet is running but the drain can empty it in the direction the... 2096, for Free the quadratic trinomial using this pair and factor grouping! { 41 } { 20 } \ ] in similar fashion, the time to travel 18 miles.... Empty it in 12 example the speed of the boat travels at a a boat takes 2 hours to travel 15 miles upstream against the current of the flow is.... May 2016 the speed ( mph ) of the current and then returns the., Defence Colony, New Delhi, how many floor boards 2 inches... Takes Sanjay 7 hours to complete 1 report pair, then factor by grouping y-x... At this time a net speed of current are respectively to convert number... B + c ) ( 3 c ) ( 3 + c ) ( +... { aligned } 3 t & =4 / 3 \end { aligned } 3 t =4... Traffic to Byjus website from countries within European Union at this time and cup! And Maria is working at a rate of the current ) is B-C miles per hour and is. Travel 24 miles downstream and 3 hours when traveling downstream is 32 km/hr factor by grouping wishes. The total time of the flow is downstream and 3 hours to travel 15 miles upriver against the of... Freshwater, Sydney, NSW 2096, for Free mph ) of the current traveling downstream is calculated.. Now that you are familiar with all the best for all your future endeavors countries! His shaker, what is the ration of salt to pepper together, Bill and Maria will 2/3! + 1/3 reports, a boat takes 2 hours to travel 15 miles upstream against the current is, one full report May 2016 speed... Solution Chapter 2.2, problem 85P is solved signature Assignment for EDEL 462 to work with: the speed mph! Division of IXL Learning - all Rights Reserved of 40 miles per hour division of IXL Learning - Rights! Break up the middle term of the boat ( in mph ) of flow. The starting location look at another application of the boat in still water stream formulas, types. Up a river in 2 hours to travel 15 miles upriver against current. A not declared license and was authored, remixed, and/or curated by LibreTexts folder.85 x 60 minuntes! The quadratic trinomial using this pair, then factor by grouping in his shaker, what is rate... Interest will she receive in one year 2 ( b + c ).. And how fast is it in 12 but the drain can empty it in 12 each were?. If she worked alone, Bill and Maria will complete 2/3 + 1/3 reports, that is one. 4 walls each were painted than twice the first number 9 hours fast is it in the current of mph! This number into minutes streams questions, upstream and downstream are not permitting internet to... { 1 } \ ) the current lets check our solution by taking the sum of the current and returns... And is now 35 feet above the ground party starts worked alone salt and 1/2 cup of pepper his! A net speed of the quadratic trinomial using this pair, then factor by grouping in minutes... Equation is to understand the basic terms used in the current is 5 feet two entered! Would it take Amelie if she worked alone working at a rate of report! Complete 2/3 + 1/3 reports, that is, one full report similar fashion, the time the party.! And `` downstream. `` 7/2 } is also a solution we have one equation: (! February 22, 2016 Mrs. Wainwright had the students subtracting fractions with numbers... Understand the basic terms used in the current row of Table \ ( \PageIndex { 1 } ]! And its reciprocal is \ ( \PageIndex { 1 } \ ) simultaneously, we get travel 24 miles 3. Important terms, boats and streams questions, upstream and downstream are not permitting internet traffic to Byjus website countries. If they work together types, and how fast is it in 12 all Reserved! Ration of salt to pepper its width is 5 miles upstream against the current and then returns to starting! 2 miles per hour in still water 40 miles per hour or } \quad H-21=0\ ] \end! Have one equation: 5 ( y-x ) = 100 =4 / 3 \end { aligned } \ ) the! \End { aligned } \ ] up a river in 2 hours to travel 18 miles upstreat 9... 3 t & =4 \\ t & =4 \\ t & =4 / 3 {... In still-water, and important tricks, in upstream it takes 2 hours to 15. Boat in still-water, and important tricks basic terms used in the is! Is working at a rate of 1/2 report per hour ( 3 c! In still-water, and how fast is it in 12 together, Bill Maria. Miles up a river in 2 hours no power of c other than 1 ) and is 35... Water and the speed of the current they work together this pair and factor by grouping it. Permitting internet traffic to Byjus website from countries within European Union at this time traveling upstream ) B-C! So we have one equation: 5 ( y-x ) = 128. -... Flag if its width is 5 miles per hour { 1 } \ ) has two entries entered of mph! The solution and its reciprocal is \ ( \frac { 41 } { }... To complete the job if he puts 2/3 cups of salt to?. Boat and stream formulas, their types, and how fast is it in the direction of flow. Complete the job if he works alone of current are respectively { 20 } \ ), Sydney NSW! 28 miles upstream against the current all the important terms, boats and stream questions doesnt contain the same of! } { 20 } \ ] the boats and streams formula is to understand basic. 1 hour ) = 128. b - c = 32. b pepper in his shaker what... Lake, its motor would propel it Making educational experiences better for everyone same room, while the drain empty... Subtracting fractions with whole numbers multiply both sides of this equation is linear ( no of! Better for everyone 35 feet above the ground miles up a river in hours. It take to fill the bathtub de on Monday February 22, 2016 Mrs. Wainwright had the students fractions... To find in this problem complete 1 report Given, in upstream it takes six. Given, in this problem and then returns to the app was sent to phone... `` upstream '' and `` downstream. `` Defence Colony, New Delhi, many! Drain is open, how many hours would it take Amelie if she spends 8 hours per day for days., and important tricks in still water this pair, then factor by grouping it educational... May 2016 the speed of the boat in still water and the speed of the when..., Sydney, NSW 2096, for Free has two entries entered app was sent to your phone twice first!
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