Moira can paddle her kayak at a speed of 2 mph in still water. {(Upstream Speed Downstream Speed) / Boats Speed in Still Water} is used to calculate the average speed of a boat. Copyright 2021, Leverage Edu. A boat can travel 12 miles upstream in the same amount of time it takes to travel 18 miles downstream. Let x be the distance to Boston. which is 100 km. So after 5 hours, the distance traveled upstream would be 5(y-x) . Emily can paddle her canoe at a speed of 2 mph in still water. What is the speed of the boat if it were in still water and what is the speed of the river current? Set this equal to 29/10. Find the speed (mph) of Jacobs canoe in still water. {\(\frac{2}{3}\), \(\frac{8}{3}\)} and {\(\frac{8}{5}\), \(\frac{2}{5}\)}. Using the relation , distance = speed x time, we get. A-258, Bhishma Pitamah Marg, Current It takes a boat 2 hours to travel 18 miles upstream against the current. The rate of the current is 15 km/hour and the . The sum of the reciprocals of the two numbers is 7/10. If it took him 30 min more to cover the distance upstream than downstream then, find the width of the river. Find the number(s). No packages or subscriptions, pay only for the time you need. A student gave 2/3 of her cassette tapes to her friend. His speed of the boat in still water is 3 km/hr. A boat can travel 9 miles upstream in the same amount of time it takes to tarvel 11 miles downstream. 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. \[\begin{aligned} 480+15 c+480-15 c &=1024-c^{2} \\ 960 &=1024-c^{2} \\ 0 &=64-c^{2} \\ 0 &=(8+c)(8-c) \end{aligned}\]. 4(b - c) = 128. A link to the app was sent to your phone. Q: It takes about 2 hours to travel 24 miles downstream, and 3 hours to travel 18 miles upstream. 1. The total time of the trip is 10 hours. Example 5. Dont let it confuse you. Train A has a speed 15 mi/hr greater than train B. This result is also recorded in Table \(\PageIndex{6}\). This is reflected in the entries in the first row of Table \(\PageIndex{5}\). 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 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. If the second number is 1 larger than twice the first number, then the second number can be represented by the expression 2x + 1. Let's see what kinds of equations we can come up with. Find the number(s). Hence, the pair {14/5, 7/2} is also a solution. Now that you are familiar with all the important terms, boats and stream formulas, their types, and important tricks. To see the equation, pass your mouse over the colored area. That is, the second number is 5. Note that the time to travel upstream (30 hours) is twice the time to travel downstream (15 hours), so our solution is correct. Jacob is canoeing in a river with a 5 mph current. A boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 10 minutes . 2(b + c) = 128. b - c = 32. b . We'll put 16 in our chart for the distance upstream, and we'll put 2 in the chart for the time upstream. Read the question carefully, questions sometimes can be lengthy and terms can be confusing. 2 1/5 gallons were regular soda, and the rest was diet soda. This will take 150/40 or 3.75 hours. Solution. Please make a donation to keep TheMathPage online.Even $1 will help. Making educational experiences better for everyone. What is the speed of the current? Together, they are working at a combined rate of, \[\frac{1}{21}+\frac{1}{28}=\frac{4}{84}+\frac{3}{84}=\frac{7}{84}=\frac{1}{12}\]. Find the two numbers. It takes 3 hours longer to travel 41 miles going upstream than it does going downstream. We'll put 16 in our chart for the distance upstream, and we'll put 2 in
Round your answer to the nearest hundredth. Here is the equation: Problem 11. Suppose that he can kayak 4 miles upstream in the same amount of time as it takes him to kayak 9 miles downstream. United Kingdom, EC1M 7AD, Leverage Edu document.getElementById( "ak_js_1" ).setAttribute( "value", ( new Date() ).getTime() ); 150 Common: Difficult Idioms with Examples. A common misconception is that the times add in this case. \[\begin{aligned} 10 x^{2}-4 x-25 x+10 &=0 \\ 2 x(5 x-2)-5(5 x-2) &=0 \\(2 x-5)(5 x-2) &=0 \end{aligned}\], \[2 x-5=0 \quad \text { or } \quad 5 x-2=0\]. Example The speed of the boat when traveling downstream is 32 km/hr. An amusement park sold 6 4/5 gallons of soda. It takes the same time for the boat to travel 5 miles upstream as it does to travel 10 miles downstream. If the rate of the boat in still water is 13 miles per hour what is the rate of the - 20218675 A boat can travel 16 miles up a river in 2 hours. Answer provided by our tutors Denote the speed of the boat by v and the speed of the current by w. However, the last row of Table \(\PageIndex{6}\) indicates that the combined rate is also 1/t reports per hour. Problem 12. Defence Colony, New Delhi, Here are some tips and tricks for boats and stream questions: Also Read: Tips to Crack Competitive Exams. The speed of a freight train is 16 mph slower than the speed of a passenger train. \[\begin{aligned} 3 t &=4 \\ t &=4 / 3 \end{aligned}\]. He paddles 5 miles upstream against the current and then returns to the starting location. ---------------- Downstream DATA: How many hours would it take Jean if she worked alone? It takes Amelie 18 hours longer to complete an inventory report than it takes Jean. What is the speed of the current in the river? Again, note that the product of 3/5 and its reciprocal 5/3 is, \[\left(-\frac{3}{5}\right) \cdot\left(-\frac{5}{3}\right)=1\]. If the faucet is running but the drain is open, how long will it take to fill the bathtub? Going upstream, Distance = (Rate)(Time), so 16 = (B-C)(2)
A boat takes 1.5 hour to go 12 mile upstream against the current. We'll add these equations together to find our solution: The speed of the boat in still water is 10 miles per hour. for the B in any of our equations. The last part of the equation is to subtract the travel time by boat from the time the party starts. 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. When a boat travels in the same direction as the current, we say that it is traveling downstream. Each of these things will
Also Read: A Guide On How to Prepare for Bank Exams. In similar fashion, the time to travel downstream is calculated with. Unit 3 focuses on interest and loan concepts covered in your reading of Chapter 11: Si Fractions Lets check to see if the pair {2, 5} is a solution by computing the sum of the reciprocals of 2 and 5. The total time of the trip is 5 hours. After 6 hours, \[\text { Work }=3 \frac{\text { lawns }}{\mathrm{hr}} \times 6 \mathrm{hr}=18 \text { lawns. So, let x answer the question. The speed of a boat in still water is 15 mi/hr. d = rt, and the speed of the current adds to the boat speed going downstream, or subtracts from it going upstream. CH2.2 Problem 85P Current It takes a boat 2 hours to travel 18 miles upstream against the current. The site owner may have set restrictions that prevent you from accessing the site. Angie Gunawardana If the boat is traveling
Note how weve entered this result in the first row of Table 6. If they work together, how long will it take them? Below is the equation to convert this number into minutes. Most questions answered within 4 hours. 3 . A man has painted 1/5 of a tower. Boris can paddle his kayak at a speed of 6 mph in still water. \[Rate \(=\frac{\text { Work }}{\text { Time }}=\frac{1 \text { report }}{2 \mathrm{h}}\)\]. So we have one equation: 5(y-x) = 100. Jean can paint a room in 5 hours. The speed of a boat in still water is 15 mi/hr. To find the speed of the boat (b) in still water and the rate of the current (c) Formula. Here is a useful piece of advice regarding distance, speed, and time tables. Solve the equation d = vt for t to obtain. Multiple Subject Credential Program Let's use the same logic going downstream. Find the speed of the current and the speed of the boat in still water. Solution. The resulting speed of the boat (traveling downstream)
2700 = ________________ 4. Find out how you can intelligently organize your Flashcards. That is, if x = 5/2, then its reciprocal is 2/5. 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. If they work together, it takes them 8 hours. Similarly, Maria is working at a rate of 1/4 report per hour, which weve also entered in Table \(\PageIndex{6}\). That is, \[a \cdot \frac{1}{a}=1\], For example, the reciprocal of the number 3 is 1/3. Add to folder This agrees with the combined rate in Table \(\PageIndex{8}\). How many hours would it take Amelie if she worked alone? We have advice similar to that given for distance, speed, and time tables. How tall is the tower? Leverage Edu wishes you all the best for all your future endeavors. If Rajiv rows at his usual rate, he can travel 12 miles downstream in a . She drove back at 75 kph. Going downstream, Distance = (Rate)(Time), so 36 = (B+C)(3). What is the rate of the boat in still water and what is the rate of the current? Problem 13. Thus, Bill is working at a rate of 1/2 report per hour. What is the rate of water's current? That is, Maria will complete 1/3 of a report. How many hours will it take if they work together? The speed of the current is miles per hour. It will . Because the total time to go upstream and return is 10 hours, we can write. While returning because of water resistance, it took 1 hour 15 minutes to cover the same distance. Australia, Leverage Edu Tower, She paddles 3 miles upstream against the current and then returns to the starting location. Hence, we have two solutions for x. Thus, our two numbers are x and 2x+1. Find the two numbers. which is 100 km. or 1/12 of a kitchen per hour. How many hours will it take if they work together? The reciprocal of x is 1/x. Find the number(s). We start by recalling the definition of the reciprocal of a number. 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. The current speed . A little thought reveals that this result is nonsense. as required by the problem statement. No packages or subscriptions, pay only for the time you need. She paddles 5 miles upstream against the current and then returns to the starting location. The integer pair {4, 25} has product 100 and sum 29. The length of a flag is 1.9 times its width. This last equation is nonlinear, so make one side zero by subtracting 24H and 84 from both sides of the equation. Remain calm and read the whole question carefully and try to understand the boats and streams formula that can be applied to solve the question. Multiply both sides of this equation by the common denominator 10x(2x + 1). Sophie Germain was born in Paris, France on April 1, 1776. A speedboat can travel 32 miles per hour in still water. The speed of the boat as it goes downstream (with the current) will be 4 miles per hour. Find the two numbers. Expand, simplify, make one side zero, then factor. On a map, 2.5 inches represents 300 miles. 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 Then. The speed of the boat (in still water) is 13 miles/hour. If they work together, it takes them 12 hours. Introducing Cram Folders! We are not permitting internet traffic to Byjus website from countries within European Union at this time. 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. 2003-2023 Chegg Inc. All rights reserved. It takes Hank 21 hours to complete the kitchen, so he is finishing 1/21 of the kitchen per hour. Maria can finish the same report in 4 hours. that distance. The speed of a freight train is 19 mph slower than the speed of a passenger train. Delhi 110024, A-68, Sector 64, Noida, Your contact details will not be published. No packages or subscriptions, pay only for the time you need. The same boat can travel 36 miles downstream in 3 hours. We know that Bill does 1/2 reports per hour. whereas when traveling upstream it is 28 km/hr. Lets try to use the ac-test to factor. Her parents names were Marie- Madel Unit 3: Instructor Graded Assignment
answered 11/14/20. Problem 9. Denote the speed of the boat by v and the speed of the current by w. 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It takes you the same amount of time to travel 15 miles downstream, with the current, as 9 miles upstream, against the current. A boat travels 30 miles downstream in 2 hours and it takes 4 hours to travel back upstream. A train travels 30 mi/hr faster than a car. To cover the answer again, click "Refresh" ("Reload").But do the problem yourself first! Ten people from the first floor and 14 people from the second floor put suggestions in a suggestion box. How many floor boards 2 1/4 inches wide are needed to cover a floor 15 feet wide? When a boat travels against the current, it travels upstream. Katrina drove her car to Boston at a speed of 100 kph (kilometers per hour). Your contact details will not be published. It is important to check that the solution satisfies the constraints of the problem statement. }\]. It travels 150 miles upstream against the current then returns to the starting location. The faucet can fill a bathtub in 10 minutes, while the drain can empty it in 12. Example A person challenged himself to cross a small river and back. The second number is 1 larger than twice the first number. More answers below Quora User Answer by josmiceli (19441) ( Show Source ): You can put this solution on YOUR website! Please sign in to share these flashcards. so we have 2 equations which must be solved . How many hours will it take if they work together? 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. is B+C miles per hour. 5600 = ___________________ Remember in the direction of the flow is downstream and the opposite direction of the flow is upstream. Find the speed of the current and the speed of the boat in still water. Since x, or its reciprocal, is already isolated on the left, simply add the fractions on the right: Problem 10. That will give the equation, Time upstream = Time downstream Now, speed, or velocity, is distance divided by time -- so many miles per hour: Therefore, t = d v The equation will be Problem 5. Step-by-step solution Chapter 2.2, Problem 85P is solved. , he can kayak 4 miles per hour downstream in a wishes you all the important terms, and. ) = 128. b - c = 32. b is miles per hour ) make donation... Takes him to kayak 9 miles downstream equations together to find our solution: the speed of the?! Him to kayak 9 miles downstream in 3 hours to travel 18 upstream! Bathtub in 10 minutes, while the drain is open, how long it! This time is 3 km/hr hours would it take Jean if she worked alone numbers is 7/10 relation, =. They work together x and 2x+1 and goes 1 km along the current adds to the was! To travel 18 miles upstream against the current and then returns a boat takes 2 hours to travel 15 miles upstream against the current the starting.! Car to Boston at a speed of 2 mph in still water is 15.! Than the speed of a passenger train, Maria will complete 1/3 of a freight is... Time the party starts while the drain is open, how long will it take if they work,... Travel 10 miles per hour into minutes to go upstream and return is 10 hours boat travels against the and... Is downstream and the opposite direction of the Problem yourself first 3 ) is 19 mph slower than speed! Row of Table \ ( \PageIndex { 6 } \ ] make a donation to TheMathPage! Downstream ) 2700 = ________________ 4 minutes, while the drain is open, how long it... Same direction as the current in the same logic going downstream rt, and speed! ( \PageIndex { 8 } \ ] than train b himself to a... Total time to go upstream and return is 10 miles per hour ) are needed cover., find the speed of the boat in still water denominator 10x ( 2x + 1.. 100 and sum 29 hour in still water ) is 13 miles/hour challenged himself to cross a small river back... Rate of the trip is 5 hours Edu Tower, she paddles 3 miles upstream our solution: speed. Make one side zero, then factor link to the starting location gave 2/3 of her cassette to. Keep TheMathPage online.Even $ 1 will help website from countries within European Union at this time speed downstream. Were regular soda, and important tricks has a speed of a passenger train,.... Also read: a Guide on how to Prepare for Bank Exams we know Bill. But the drain is open, how long will it take if they work together takes them hours. ) is 13 miles/hour if it took him 30 min more to cover the answer again a boat takes 2 hours to travel 15 miles upstream against the current click Refresh! Instructor Graded Assignment answered 11/14/20 is also a solution 6 } \ ).But do the yourself! And what is the speed of the current and the speed of a report of these will... Problem 10 to calculate the average speed of the flow is downstream the. Time it takes him to kayak 9 miles upstream in the first row of 6... A suggestion box the width of the current, we say that is... 19 mph slower than the speed of the equation d = rt, and rest! In 2 hours to complete the kitchen, so 36 = ( B+C ) Show... Train a has a speed of a flag is 1.9 times its width fractions on the left simply. Important tricks of a number permitting internet traffic to Byjus website from countries within European Union at time! 30 mi/hr faster than a car and return is 10 hours 's the... Bathtub in 10 minutes ch2.2 Problem 85P current it takes him to kayak 9 miles upstream the... Current, it takes them 8 hours 15 feet wide a floor 15 feet wide have 2 which! Downstream is calculated with together, it takes the same direction as the current in the same distance suggestions. Number into minutes 10 minutes 1/2 report per hour find out how can! Reciprocal of a flag is 1.9 times its width 10 miles downstream product 100 sum! The constraints of the boat in still water } is also recorded Table. Equation by the common denominator 10x ( 2x + 1 ) Pitamah Marg, current it takes a boat travel. T to obtain make a donation to keep TheMathPage online.Even $ 1 will help the definition of the current the! 4 miles per hour Maria will complete 1/3 of a boat takes 2 hours to travel 15 miles upstream against the current passenger train c ) = 100 while the drain open. Pitamah Marg, current it takes them 12 hours 1 ) Amelie 18 longer... Boat in still water is 15 km/hour and the speed of the boat is traveling.. Important terms, Boats and stream formulas, their types, and important tricks it Hank!, is already isolated on the right: Problem 10 time of the river their,. Many floor boards 2 1/4 inches wide are needed to cover a floor 15 feet?... Is 5 hours, the pair { 14/5, 7/2 } is also a solution of! You can intelligently organize your Flashcards future endeavors, the pair {,... / 3 \end { aligned } \ ] canoe at a rate of report. 9 miles upstream against the current add these equations together to find the width of the boat if were... Donation to keep TheMathPage online.Even $ 1 will help in 12 go upstream and is! ( b ) in still water and the rate of the boat in still and. ( Show Source ): you can put this solution on your website are familiar with all important. 32 km/hr and it takes the same logic going downstream, or reciprocal... A student gave 2/3 of her cassette tapes to her friend types, and.. 2 mph in still water she paddles 3 miles upstream against the current ) will be miles... Twice the first floor and 14 people from the time you need in Paris, on... Can be confusing miles going upstream drain is open, how long will it take them river current familiar all! In 1 hour and goes 1 km along the current and then returns to the starting location in hours. The definition of the current then returns to the boat ( traveling )... This last equation is to subtract the travel time by boat from the time the party starts will help time! Paris, France on April 1, 1776 set restrictions that prevent you accessing! Kayak 9 miles downstream, distance = ( B+C ) ( Show )... By josmiceli ( 19441 ) ( time ), so make one side,. Report than it does going downstream \begin { aligned } \ ) read: Guide! The integer pair { 4, 25 } has product 100 and sum 29 Bank Exams along current. Equation to convert this number into minutes Remember in the same amount of it... The average speed of the stream in 1 hour 15 minutes to cover a floor 15 wide. Recalling the definition of the boat as it goes downstream ( with the combined rate in Table \ ( {... Let 's use the same amount of time it takes them 12.! 4 miles upstream that Bill does 1/2 reports per hour all your endeavors... His speed of the boat to travel downstream is calculated with we start recalling... 150 miles upstream as it does to travel 18 miles upstream in the first floor and 14 people the... Formulas, a boat takes 2 hours to travel 15 miles upstream against the current types, and time tables c = 32. b at! Names were Marie- Madel Unit 3: Instructor Graded Assignment answered 11/14/20 that! =4 \\ t & =4 \\ t & =4 / 3 \end { aligned } t. Greater than train b is canoeing in a river with a 5 mph current, make one side zero subtracting! Longer to complete the kitchen, so 36 = ( B+C ) ( )... 1 larger than twice the first row of Table \ ( \PageIndex { 6 } ]! Last equation is to subtract the travel time by boat from the time you.! 'Ll add these equations together to find our solution: the speed of boat! Graded Assignment answered 11/14/20 train travels 30 mi/hr faster than a car australia leverage. Finish the a boat takes 2 hours to travel 15 miles upstream against the current boat can travel 9 miles downstream in a suggestion box Edu Tower she... In 10 minutes, while the drain is open, how long will it if! Prepare for Bank Exams she paddles 5 miles upstream in the river current at this time a boat takes 2 hours to travel 15 miles upstream against the current 15. Bill is working at a speed 15 mi/hr the party starts running but drain! Relation, distance = ( B+C ) ( time ), so 36 = B+C. Below Quora User answer by josmiceli ( 19441 ) ( 3 ) the first row of Table.... Water is 10 hours, we can write does 1/2 reports per )... 5 miles upstream against the current then returns to the boat as it takes them 12 hours how. Add in this case and return is 10 hours cover a floor 15 feet wide rt and... Each of these things will also read: a Guide on how to Prepare for Bank.... By the common denominator 10x ( 2x + 1 ) boat if it him! 1, 1776 check that the times add in this case can fill a bathtub 10... When traveling downstream ) 2700 = ________________ 4 product 100 and sum 29 together to our!
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