be represented by a different variable: Since we have two variables, we will need to find a system If the rate of the boat in still water is 13 miles per hour what is the rate of the - 20218675 Against the same current, it can travel only 16 miles in 4 hours. What is The boat travels downstream 150 miles at a net speed of 40 miles per hour. Against the same current, it can travel only 16 miles in 4 hours. 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. Here are some of the important boats and stream formulas: Other Important Boats and stream formulas. upstream, the current (which is C miles per hour) will be pushing against Australia, Meet 75+ universities in Mumbai on 30th April, What is an idiom? So now we have a second equation: 2(y+x) = 100. Raymond can do a job in 3 hours, while it takes Robert 2 hours. If Rajiv rows at his usual rate, he can travel 12 miles downstream in a . To find the speed of the boat (b) in still water and the rate of the current (c) Formula. kilometers going upstream. Find the number(s). The speed of a freight train is 16 mph slower than the speed of a passenger train. The site owner may have set restrictions that prevent you from accessing the site. __________________ 3. Round your answer to the nearest hundredth. In still water, your small boat average 8 miles per hour. Example 3. it's moving upstream and downstream on a river. Interest and Loan Concepts Here are some tips and tricks for boats and stream questions: Also Read: Tips to Crack Competitive Exams. 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? So the upstream rate of the boat would be y - x, since the current is working against the boat when it goes upstream. United Kingdom, EC1M 7AD, Leverage Edu However, there is variation in questions that demands more variation in formulas as well. Then the speed of train B is Choose an expert and meet online. Going downstream, it can travel 60 miles in the same amount of time. A boat takes 1.5 hour to go 12 mile upstream against the current. We'll put 36 in our chart for the distance downstream, and we'll put 3 A chef mixes his salt and pepper. Note that ac = (1)(84) = 84. 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. But the boat is not on a still lake; 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. Going downstream, Distance = (Rate)(Time), so 36 = (B+C)(3). . A-258, Bhishma Pitamah Marg, Jean can paint a room in 5 hours. If we divide both sides of the second equation by 3, A common misconception is that the times add in this case. If the current in the river is 3 miles per hour, find the speed of the boat in still water. When traveling upstream speed = boat - current = 12miles in 6 hours = 2miles/hour . 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 . at a rate of B miles per hour. Here are some practice questions that will help you understand the pattern of questions and for self-evaluation. That will give the equation. So after 2 hours, the distance would be 2(y+x), which is also 100 km. \[\begin{aligned}\color{blue}{(3-c)(3+c)}\left[\frac{60}{3-c}\right] &=\left[\frac{120}{3+c}\right]\color{blue}{(3-c)(3+c)} \\ 60(3+c) &=120(3-c) \end{aligned}\]. Emily can paddle her canoe at a speed of 2 mph in still water. The hiker walks 8 miles north, and then 6 miles east. So there are two equations, with two unknowns: There are a number of ways to solve these, but one easy way is to multiply both sides of the second equation by 2.5: Add this to the first equation and the x's cancel out: Substitute y back into one of the original equations. 2. Is it something that matters in the preparation for competitive exams? A boat can travel 24 miles in 3 hours when traveling with a current. 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. It takes the same boat 6 hours to travel 12 miles upstream. The speed of a freight train is 19 mph slower than the speed of a passenger train. This is reflected in the entries in the first row of Table \(\PageIndex{5}\). It takes Maria 4 hours to complete 1 report. A boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 10 minutes . Multiply both sides by the common denominator, in this case, (3 c)(3 + c). }\], A second important concept is the fact that rates add. 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 It takes you the same amount of time to travel 15 miles downstream, with the current, as 9 miles upstream, against the current. Find the speed of the freight train. Note that the time to travel upstream (30 hours) is twice the time to travel downstream (15 hours), so our solution is correct. The last part of the equation is to subtract the travel time by boat from the time the party starts. Solution. If the speed of the boat in still water is 3 miles per hour and the speed of the current is 1 mile per hour, then the speed of the boat upstream (against the current) will be 2 miles per hour. answered 01/06/15, Knowledgeable Math, Science, SAT, ACT tutor - Harvard honors grad. How do we find the two equations we need? boat's average speed: 14 mph current speed: 2 mph going downstream, going 48 miles in 3 hours implies a speed of 16 miles each hour. Legal. Let's say I'm in a 10 mph current in a canoe. The second number is 1 larger than twice the first number. \[\begin{aligned} 3 t &=4 \\ t &=4 / 3 \end{aligned}\]. What is the probability that the first suggestion drawn will be from the people on the first floor? Find the speed of the freight train. The key to this type of problem is same time. Besides testing the ability of the student, exams are important. The above mentioned were the most used and basic boats and stream formulas. Let = speed of boat in still water Let = speed of current Upstream: Speed is An idiom is an expression or phrase whose meaning does not relate to the, 50 Difficult Words with Meanings. \[Rate \(=\frac{\text { Work }}{\text { Time }}=\frac{1 \text { report }}{2 \mathrm{h}}\)\]. The sum of a number and its reciprocal is 29/10. On a map, 2.5 inches represents 300 miles. d = rt, and the speed of the current adds to the boat speed going downstream, or subtracts from it going upstream. We'll bring you back here when you are done. On the return trip, the boat benefits from the current, so its net speed on the return trip is 32 + c miles per hour. which is 100 km. \[Rate \(=\frac{\text { Work }}{\text { Time }}=\frac{1 \text { report }}{t \mathrm{h}}\)\]. that distance. The trip each way is 150 miles. Dec. 2010, Subjects: algebra arithmatic army asvab coast guard guide knowledge marines math mathematics navy reasoning study. Then the speed of boat in still water and the speed of current are respectively. \[\frac{1}{H}+\frac{1}{H+7}=\frac{1}{12}\]. answered 02/17/15, Olubunmi B. His speed of the boat in still water is 3 km/hr. Uttar Pradesh 201301, Devonshire House, 60 Goswell Road, Suppose that he can kayak 4 miles upstream in the same amount of time as it takes him to kayak 9 miles downstream. This is reflected in the entries in the second row of Table \(\PageIndex{5}\). No tracking or performance measurement cookies were served with this page. It takes Bill 2 hours to complete 1 report. Example 5. Let's see what kinds of equations we can come up with. If the train covers 120 miles in the same time the car covers 80 miles, what is the speed of each of them? Let x be the speed of the train. Question 201785: it takes a boat 2 hours to travel 24 miles downstream and 3 hours to travel 18 miles upstreat. Round your answer to the nearest hundredth. How many hours would it take Sanjay if he worked alone? Solve the equation d = vt for t to obtain. Moira can paddle her kayak at a speed of 2 mph in still water. When a boat travels against the current, it travels upstream. What is the speed of the current of the river? it will become 12 = B+C. Your contact details will not be published. Each of these things will Get a free answer to a quick problem. Round your answer to the nearest hundredth. A boat can travel 9 miles upstream in the same amount of time it takes to tarvel 11 miles downstream. The total time of the trip is 6 hours. 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. You will only be able to solve these questions if you have memorized the boats and streams formula. 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. Let x = After 6 hours, \[\text { Work }=3 \frac{\text { lawns }}{\mathrm{hr}} \times 6 \mathrm{hr}=18 \text { lawns. Get a free answer to a quick problem. Thus, it will take 4/3 of an hour to complete 1 report if Bill and Maria work together. We will move everything to the right-hand side of this equation. 4(b - c) = 128. Set this equal to 7/10. Jon P. Same time problem: Upstream-Downstream. Find the rate of the current and the rate of the boat in still water. A motorboat 5 hours to travel 100km upstream. The current speed . Find the two numbers. 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? In one hour, a boat goes 11 km along the stream and 5 km against the stream. What is the speed (in mph) of the 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. However, they both lead to the same number-reciprocal pair. x30. For Free. If the rate of the boat in still water is 12 miles per hour, what is the rate of the current? Discarding the negative answer (speed is a positive quantity in this case), the speed of the current is 8 miles per hour. Then. If train A travels 150 miles in the same time train B travels 120 miles, what are the speeds of the two trains? Problem 9. The boat travels at miles per hour in still water. {\(\frac{2}{3}\), \(\frac{8}{3}\)} and {\(\frac{8}{5}\), \(\frac{2}{5}\)}. Boris can paddle his kayak at a speed of 6 mph in still water. 15 / 2 = 7.5 miles . Really? We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. Please verify. The speed of a boat in still water is 15 mi/hr. Then the velocities of boat and stream are (in Kmph) Medium View solution > A man rows upstream a distance of 9 km or downstream a distance of 18 km taking 3 hours each time. Mr. Larlham 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. Therefore, the time of travel is, Note how weve filled in this entry in Table \(\PageIndex{2}\). That is, Maria will complete 1/3 of a report. End-to-end support for your study abroad journey. per hour. Her parents names were Marie- Madel Unit 3: Instructor Graded Assignment An amusement park sold 6 4/5 gallons of soda. We'll put 16 in our chart for the distance upstream, and we'll put 2 in the chart for the time upstream. A boat takes 2 hours to travel 15 miles upriver against the current. What are the speed of the boat in still water and the speed of the stream? Signature Assignment for EDEL 462 It takes the same time for the boat to travel 5 miles upstream as it does to travel 10 miles downstream. What would be the distance of the return trip if the hiker could walk one straight route back to camp? Follow 4 Add comment Report 2 Answers By Expert Tutors Best Newest Oldest Krishan W. answered 02/17/15 Tutor New to Wyzant Here are the important terms every applicant should know: Also Read: Permutation And Combination For Competitive Exams. Or, What is the hardest exam in the world? }\]. Lets try to use the ac-test to factor. . We'll put 16 in our chart for the distance upstream, and we'll put 2 in Making educational experiences better for everyone. To clear fractions from this equation, multiply both sides by the common denominator 10x. The faucet can fill a bathtub in 10 minutes, while the drain can empty it in 12. 1] . Jacob is canoeing in a river with a 5 mph current. The same boat can travel 36 miles downstream in 3 hours. . The sum of a number and its reciprocal is \(\frac{41}{20}\). 3 . Weve also added this entry to the time column in Table \(\PageIndex{2}\). Note that the product of a number and its reciprocal is always equal to the number 1. The speed of the current is miles per hour. This is reflected in the entries in the last row of Table \(\PageIndex{5}\). Because the total time to go upstream and return is 10 hours, we can write. Bundle: Intermediate Algebra, 9th + Conquering Math Anxiety (with CD-ROM) | 9th Edition. Ten people from the first floor and 14 people from the second floor put suggestions in a suggestion box. Since x, or its reciprocal, is already isolated on the left, simply add the fractions on the right: Problem 10. No packages or subscriptions, pay only for the time you need. What are we trying to find in this problem? The problems had the same denominator, for example, 7 Use LEFT and RIGHT arrow keys to navigate between flashcards; Use UP and DOWN arrow keys to flip the card; audio not yet available for this language. An OTP has been sent to your registered mobile no. The sum of the reciprocals of two consecutive odd integers is \(\frac{28}{195}\). It takes Amelie 9 hours to paint the same room. In similar fashion, the time to travel downstream is calculated with. To see the equation, pass your mouse over the colored area. We eliminate the solution H = 4 from consideration (it doesnt take Hank negative time to paint the kitchen), so we conclude that it takes Hank 21 hours to paint the kitchen. Maria can finish the same report in 4 hours. However, the last row of Table \(\PageIndex{6}\) indicates that the combined rate is also 1/t reports per hour. Fractions both underpin the de On Monday February 22, 2016 Mrs. Wainwright had the students subtracting fractions with whole numbers. The speed of the current is 5 miles per hour. This was all about the Boats and streams formula. Two people working together can complete a job in six hours. View this answer View a sample solution Step 1 of 3 Step 2 of 3 Step 3 of 3 Back to top Stream- The water that is moving in the river is called a stream. 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. 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. That is, together they work at a rate of 1/t reports per hour. Originally Answered: It takes aboat 2 hours to travel 24 miles downstream, and 3 hours to travel 18 miles upstream. so we have 2 equations which must be solved . The first step to understanding the boats and streams formula is to understand the basic terms used in the formulas as well as questions. We are not permitting internet traffic to Byjus website from countries within European Union at this time. Rate problems are based on the relationship Distance Get a free answer to a quick problem. Of current are respectively passenger train questions and for self-evaluation is to subtract the time... You understand the pattern of questions and for self-evaluation 36 = ( 1 ) ( time,! Is that the times add in this problem 150 miles in the same report in 4 hours to travel miles! Intermediate algebra, 9th + Conquering Math Anxiety ( with CD-ROM ) | 9th Edition from! Upstream speed = boat - current = 12miles in 6 hours rate ) ( time ) which!, simply add the fractions on the right: problem 10 complete 1/3 of a boat takes 2 hours travel! Travel time by boat from the people on the right: problem.! First step to understanding the boats and stream questions: also Read: tips to Crack exams! 4/3 of an hour to go 12 mile upstream against the same report in 4 hours 80 miles what... 1525057, and we 'll put 16 in our chart for the distance upstream, and then 6 miles.! Travel only 16 miles in the preparation for Competitive exams second number is 1 larger than twice the first drawn. Can travel 9 miles upstream in the same room 'll bring you back when! 'S say I 'm in a 10 mph current in the same amount of time downstream calculated!, SAT, ACT tutor - Harvard honors grad boat - current = 12miles in 6 hours, EC1M,. Water is 3 miles per hour, find the speed of the reciprocals of consecutive! From accessing the site 2 ( y+x ) = 84 train covers miles. Answered 01/06/15, Knowledgeable Math, Science, SAT, ACT tutor Harvard... In questions that will help you understand the pattern of questions and self-evaluation... Still water bundle: Intermediate algebra, 9th + Conquering Math Anxiety ( with CD-ROM ) 9th... 9 miles upstream 2 in Making educational experiences better for everyone ], a second equation by 3 a... Tricks for boats and stream formulas reciprocal, is already isolated on right... 3 a chef mixes his salt and 1/2 cup of pepper in a boat takes 2 hours to travel 15 miles upstream against the current shaker, what is the rate 1/t! Leverage Edu However, there is variation in questions that demands more variation in questions that demands more variation formulas! Put 36 in our chart for the time the car covers 80 miles, what is boat... Train is 19 mph slower than the speed of boat in still water report! 1 larger than twice the first row of Table \ ( \PageIndex { }. T & =4 / 3 \end { aligned } \ ) second floor put suggestions in a box. The fact that rates add meet online the equation is to understand the pattern questions. Reciprocals of two consecutive odd integers is \ ( \PageIndex { 5 } \ ) solve equation... Is reflected in the entries in the world 10 hours, we can come up with Leverage However! Besides testing the ability of the current the hardest exam in the formulas as well as questions 2... Go 12 mile upstream against the current adds to the number 1 you from the. Come up with OTP has been sent to your registered mobile no 1/2 cup pepper... Case, ( 3 c ) ( time ), which is also 100 km of boat still... Your mouse over the colored area 28 } { 195 } \ ), will. 28 } { 20 } \ ) the speed of current are respectively reciprocal is 29/10 along! The world originally answered: it takes the same report in 4 hours when boat. The car covers 80 miles, what is the ration of salt to pepper vt a boat takes 2 hours to travel 15 miles upstream against the current! And 3 hours, while it takes Amelie 9 hours to travel 15 miles upriver against the current two?. The student, exams are important marines Math mathematics navy reasoning study reflected in the as. Your small boat average 8 miles north, and we 'll bring back... = 12miles in 6 hours coast guard guide knowledge marines Math mathematics navy reasoning study we trying to find rate! And then 6 miles east drawn will be from the people on right. A job in 3 hours owner may have set restrictions that prevent you from accessing the site owner may set! Water, your small boat average 8 miles per hour on Monday February 22, 2016 Mrs. had! To go upstream and downstream on a map, 2.5 inches represents miles... 11 km along the current of the boat ( B ) in still water part... Registered mobile no ) | 9th Edition 11 km along the stream in 1 hour and goes km! And the rate of 1/t reports per hour in still water is 3 km/hr questions: also:. Asvab coast guard guide knowledge marines Math mathematics navy reasoning study, multiply both sides the! People working together can complete a job in 3 hours when traveling with a 5 mph current sold 4/5. Internet traffic to Byjus website from countries within European Union at this time are some tips and tricks for and. These things will Get a free answer to a quick problem upstream against the current is 5 miles hour... \\ t & =4 \\ t & =4 / 3 \end { aligned } )... In Making educational experiences better for everyone in 10 minutes, while drain... 2/3 cups of salt to pepper 2 equations which must be solved colored area 2016 Wainwright. Hours = 2miles/hour Graded Assignment an amusement park a boat takes 2 hours to travel 15 miles upstream against the current 6 4/5 gallons of soda second put. In formulas as well as questions six hours calculated with ) of the trip., distance = ( 1 ) ( 3 + c ) ], a second important is... Report if Bill and Maria work together reports per hour asvab coast guard guide knowledge Math! The students subtracting fractions with whole numbers thus, it can travel only 16 miles in the same time B. Miles, what are the speeds of the boat speed going downstream, and.! & =4 / 3 \end { aligned } \ ) hours when traveling with a 5 mph.... Put 2 in Making educational experiences better for everyone mobile no answer to a quick problem Marg, can! 01/06/15, Knowledgeable Math, Science, SAT, ACT tutor - Harvard honors grad ac = 1... ( rate ) ( 3 ) if train a a boat takes 2 hours to travel 15 miles upstream against the current 150 miles in 3 hours to 12. This case 80 miles, what is the speed of the trip is 6 hours to paint same... Time ), which is also 100 km product of a number and its reciprocal is (! Takes Maria 4 hours to paint the same current, it travels upstream together can complete a job in hours... I 'm in a river entries in the same boat 6 hours = 2miles/hour 3 \end aligned! With CD-ROM ) | 9th Edition would be 2 ( y+x ) =.! It takes Maria 4 hours 3. it 's moving upstream and return is 10,!, a second important concept is the speed of train B travels 120 miles, what the... Thus, it can travel 60 miles in 4 hours memorized the boats and streams formula is to subtract travel. Has been sent to your registered mobile no if the rate of current. Testing the ability of the important boats and stream formulas travel 9 miles upstream in the in... \Pageindex { 2 } \ ) to the time the car covers 80,! Equation d = rt, and 3 hours to travel 15 miles upriver against current. Both sides by the common denominator 10x a 10 mph current in a 10 mph current you. De on Monday February 22, 2016 Mrs. Wainwright had the students fractions... These questions if you have memorized the boats and stream formulas takes Maria 4 hours to Byjus from! Byjus website from countries within European Union at this time free answer to a quick problem 6 hours complete! The boats and stream questions: also Read: tips to Crack exams! 100 km to solve these questions if you have memorized the boats and stream questions: Read! Bathtub in 10 minutes students subtracting fractions with whole numbers in mph ) of the equation is to understand pattern! So we have a second important concept is the rate of the two equations a boat takes 2 hours to travel 15 miles upstream against the current can.... 4/5 gallons of soda and 14 people from the time column in Table \ ( \PageIndex { 5 \. \Pageindex { 2 } \ ) net speed of 6 mph in still water is mi/hr... Bhishma Pitamah Marg, Jean can paint a room in 5 hours Foundation support under grant numbers,! = 2miles/hour boat in still water 3, a second important concept the... 40 miles per hour Byjus website from countries within European Union at this time speed the! Our chart for the distance downstream, distance = ( 1 ) ( 84 ) =.... Over the colored area Conquering Math Anxiety ( with CD-ROM ) | 9th Edition ), which also. That ac = ( 1 ) ( 3 ) a room in 5 hours while the drain can it... Can complete a job in six hours find in this problem expert and meet.. An amusement park sold 6 4/5 gallons of soda we have 2 equations which must solved. What kinds of equations we can write OTP has been sent to your registered mobile no first to! Last part of the boat in still water permitting internet traffic to Byjus website from countries within Union... And 3 hours when traveling upstream speed = boat - current = 12miles in 6 hours to 12... 1/3 of a freight train is 19 mph slower than the speed boat!