Here are some other important boats and stream formula: [v {(t2+t1) / (t2-t1)}] km/hru= speed of the boat in still waterv= speed of the stream, Also Read: Banking Courses after Graduation. our information in it: A boat can travel 16 miles up a river in 2 hours. 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. 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. If we let c represent the speed of the current in the river, then the boats speed upstream (against the current) is 3 c, while the boats speed downstream (with the current) is 3 + c. Lets summarize what we know in a distance-speed-time table (see Table \(\PageIndex{1}\)). In our discussion above, we pointed out 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 A woman deposits $600 into an account that pays 5 1/4 interest per year. Find the speed of the freight train. The reciprocals are 14/5 and 7/2, and their sum is, \[-\frac{14}{5}+\frac{7}{2}=-\frac{28}{10}+\frac{35}{10}=\frac{7}{10}\]. \[x=\frac{5}{2} \quad \text { or } \quad x=\frac{2}{5}\]. Problem 13. This was all about the Boats and streams formula. A boat can travel 16 miles up a river in 2 hours. Solution. For example, in the first row, d = 60 miles and v = 3 c miles per hour. }\], A second important concept is the fact that rates add. It takes Ricardo 8 hours longer to complete an inventory report than it takes Amelie. A student gave 2/3 of her cassette tapes to her friend. There are two numbers. At last, practice makes the students perfect. If the second number is 1 larger than twice the first number, then the second number can be represented by the expression 2x + 1. A painter can paint 4 walls per hour. Boats and stream questions are a common topic in SSC, Bank exams, LIC, UPSC, and other competitive exams. It will take 30 hours to travel 60 miles at this rate. Thus, our two numbers are x and 2x+1. A boat travels 24 km upstream in 6 hours and 20 km downstream in 4 hours. Again, it is very important that we check this result. The speed of a boat in still water is 15 mi/hr. answered 11/14/20, Mathematics Teacher - NCLB Highly Qualified. Total time problem. We'll put 36 in our chart for the distance downstream, and we'll put 3 in the chart for the time downstream. What is the speed of the current? Let's use the same logic going downstream. Going upstream, Distance = (Rate)(Time), so 16 = (B-C)(2)
document.getElementById( "ak_js_1" ).setAttribute( "value", ( new Date() ).getTime() ); 150 Common: Difficult Idioms with Examples. Then the speed of the car is
A boat takes 2 hours to travel 15 miles upriver against the current. Note that ac = (1)(84) = 84. Solution. If 180 cubic centimeters of water is frozen, by how many cubic centimeters will its volume increase? Still Water- When the water is stationary i.e. { "3.17.01:_Introducing_Rational_Functions" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.
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This will take 150/24 or 6.25 hours. This leads to the entries in Table \(\PageIndex{7}\). Please upgrade to Cram Premium to create hundreds of folders! That will give the equation. Moira can paddle her kayak at a speed of 2 mph in still water. 1] . 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. What is the speed (in mph) of the current? A man has painted 1/5 of a tower. So we have one equation: 5(y-x) = 100. 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. Freshwater, Sydney, NSW 2096, Jean can paint a room in 5 hours. Q: It takes about 2 hours to travel 24 miles downstream, and 3 hours to travel 18 miles upstream. Unit 3 focuses on interest and loan concepts covered in your reading of Chapter 11: Si Fractions for the B in any of our equations. Leverage Edu wishes you all the best for all your future endeavors. All boat and stream questions are not the same, they can be classified into 4 types distance, average speed, speed, and time-based questions. That is, the second number is 5. A little thought reveals that this result is nonsense. ------- Upstream DATA: distance = 12 miles ; rate = b-3 mph ; time = 12/ (b-3) hrs. A train travels 30 mi/hr faster than a car. It takes Amelie 9 hours to paint the same room. Find the two numbers. Every applicant should memorize these and should be on fingertips. Find the number(s). We'll choose the easiest equation
\[\begin{array}{l}{0=H^{2}+7 H-24 H-84} \\ {0=H^{2}-17 H-84}\end{array}\]. She drove back at 75 kph. Moira can paddle her kayak at a speed of 2 mph in still water. If the rate of the boat in still water is 13 miles per hour what is the rate of the - 20218675 Or, What is the hardest exam in the world? Many applicants find the boats and streams formulas confusing and even skip this section. Here is a useful piece of advice regarding distance, speed, and time tables. Each of these linear equations is easily solved. A hiker follows a trail that goes from camp to lake. A boat takes 1.5 hour to go 12 mile upstream against the current. 1] . Solving the system of equations simultaneously, we get. Then. The speed of a boat in still water is 15 mi/hr. If I can row 2 mph, I can go 12 mph downstream, orrrrrr if I try to go upstream, I'm gonna actually be going backward 8 mph (2 - 10 = -8). The sum of the reciprocals of two consecutive odd integers is \(\frac{28}{195}\). If the boat travels 8 miles downstream in the same time it takes to travel 4 miles upstream, what is the speed of the current? The sum of a number and its reciprocal is 29/10. 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. This is reflected in the entries in the first row of Table \(\PageIndex{5}\). Find the two numbers. Thus if b is the speed of the boat in still water, and c is the speed of the current, then its total speed is. If the current in the river is 3 miles per hour, find the speed of the boat in still water. \[\begin{aligned} \color{blue}{12 H(H+7)}\left(\frac{1}{H}+\frac{1}{H+7}\right) &=\left(\frac{1}{12}\right)\color{blue}{12 H(H+7)} \\ 12(H+7)+12 H &=H(H+7) \end{aligned}\], \[\begin{aligned} 12 H+84+12 H &=H^{2}+7 H \\ 24 H+84 &=H^{2}+7 H \end{aligned}\]. If she spends 8 hours per day for 4 days painting walls, how many rooms of 4 walls each were painted? The speed of a freight train is 20 mph slower than the speed of a passenger train. Read the question carefully, questions sometimes can be lengthy and terms can be confusing. Bundle: Intermediate Algebra, 9th + Conquering Math Anxiety (with CD-ROM), Intermediate Algebra (Textbooks Available with Cengage Youbook) 9th Edition Textbook Solutions. Find out how you can intelligently organize your Flashcards. How far away was Boston? However, they both lead to the same number-reciprocal pair. What is the speed of the boat if it were in still water and what is the speed of the river current? It takes Ricardo 12 hours longer to complete an inventory report than it takes Sanjay. Let x represent the first number. Let x be the speed of the train. Find the two numbers. That is, Bill will complete 2/3 of a report. Lets check to see if the pair {2, 5} is a solution by computing the sum of the reciprocals of 2 and 5. Now let's think about the rate the boat travels. \[\frac{1}{H}+\frac{1}{H+7}=\frac{1}{12}\]. A boat takes 2 hours to travel 15 miles upriver against the current. Delhi 110024, A-68, Sector 64, Noida, \[\begin{aligned}\color{blue}{(4 t)}\left[\frac{1}{2}+\frac{1}{4}\right] &=\left[\frac{1}{t}\right]\color{blue}{(4 t)} \\ 2 t+t &=4 \end{aligned}\]. Choose an expert and meet online. A link to the app was sent to your phone. If the speed of the boat in still water is 15 miles per hour, what is the speed of the current? The hiker walks 8 miles north, and then 6 miles east. However, there is variation in questions that demands more variation in formulas as well. If Rajiv rows at his usual rate, he can travel 12 miles downstream in a . Besides testing the ability of the student, exams are important. Leverage Edu Tower, Let's say I'm in a 10 mph current in a canoe. Emily can paddle her canoe at a speed of 2 mph in still water. Find the speed (mph) of Boriss kayak in still water. Find the speed of the freight train. Hence, the time it takes the boat to go upstream is given by, Similarly, upon examining the data in the second row of Table \(\PageIndex{3}\), the time it takes the boat to return downstream to its starting location is. If we divide both sides of the first equation by 2, it
This equation is linear (no power of t other than 1) and is easily solved. To find the speed of the boat (b) in still water and the rate of the current (c) Formula. Thus, Bill is working at a rate of 1/2 report per hour. A motorboat 5 hours to travel 100km upstream. Therefore, The rate of current is, Hence, The required rate of current is 1.6. Australia, Leverage Edu Tower, 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. }\]. If they work together, it takes them 10 hours. While returning because of water resistance, it took 1 hour 15 minutes to cover the same distance. Find the speed of the current and the speed of the boat in still water. Example The speed of the boat when traveling downstream is 32 km/hr. If the speed of the boat in still water is 10 mph, the speed of the stream is: A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream. The total time of the trip is 10 hours. Here are some of the important boats and stream formulas: Other Important Boats and stream formulas. Mark M. Lets try to use the ac-test to factor. a. On the other hand, if x = 2/5, then its reciprocal is 5/2. whereas when traveling upstream it is 28 km/hr. Let x =
What is the rate of water's current? distance = rate * time UPSTREAM 9 r-3 DOWNSTREAM 11 r+3 Time= distance/rate EQUATION: Time up = Time down When a boat travels against the current, it travels upstream. The sum of a number and twice its reciprocal is \(\frac{9}{2}\). How long does it take him to go 5 km in stationary water? Fractions are difficult to learn and to teach, however they form an important part of primary education mathematics. The same boat can travel 36 miles downstream in 3 hours. Most questions answered within 4 hours. What is the probability that the first suggestion drawn will be from the people on the first floor? What is the speed of the boat in still water? Boris can paddle his kayak at a speed of 6 mph in still water. The boat travels at miles per hour in still water. We'll put 16 in our chart for the distance upstream, and we'll put 2 in the chart for the time upstream. How many hours will it take if they work together? Solution. It is important to check that the solution satisfies the constraints of the problem statement. That is, together they work at a rate of 1/t reports per hour. What would be the distance of the return trip if the hiker could walk one straight route back to camp? If the speed of the boat in still water is 15 miles per hour, what is the speed of the current? 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. It takes Amelie 10 hours to paint the same room. What is the rate of the boat in still water and what is the rate of the current? Problem 8. What proportion of the kites are blue? How many hours would it take Sanjay if he worked alone? No packages or subscriptions, pay only for the time you need. The rate of the current is 15 km/hour and the . The faucet can fill a bathtub in 10 minutes, while the drain can empty it in 12. Let H represent the time it take Hank to complete the job of painting the kitchen when he works alone. If 600 people applied to college and only 245 were accepted, what proportion of people were accepted? 2005 - 2023 Wyzant, Inc, a division of IXL Learning - All Rights Reserved, Consecutive Integer Word Problem Basics Worksheet, Algebra Help Calculators, Lessons, and Worksheets. For the latest updates around study blogs, you can follow us on Instagram, Twitter, Facebook and also subscribe to our newsletter. On a map, 2.5 inches represents 300 miles. The return trip takes2. hours going downstream. Katrina drove her car to Boston at a speed of 100 kph (kilometers per hour). Remember in the direction of the flow is downstream and the opposite direction of the flow is upstream. Weve entered this data in Table \(\PageIndex{3}\). That is, \[\text { Work }=\text { Rate } \times \text { Time. The third entry in each row is time. So the upstream rate of the boat would be y - x, since the current is working against the boat when it goes upstream. Problem 6. Note that the time to travel upstream (30 hours) is twice the time to travel downstream (15 hours), so our solution is correct. 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. We know that Bill does 1/2 reports per hour. (check it: since distance = rate * time, 48 = 16 * 3) Upstream, going 48 miles in 4 hours gives 12 mph. \[\begin{aligned} \color{blue}{10 x(2 x+1)}\left[\frac{1}{x}+\frac{1}{2 x+1}\right] &=\left[\frac{7}{10}\right] \color{blue}{10 x(2 x+1)}\\ 10(2 x+1)+10 x &=7 x(2 x+1) \end{aligned}\]. Jacob is canoeing in a river with a 5 mph current. In one hour, a boat goes 11 km along the stream and 5 km against the stream. 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. at a rate of B miles per hour. Example 4. Her parents names were Marie- Madel Unit 3: Instructor Graded Assignment
Find the rate of the current and the rate of the boat in still water. How many hours would it take Amelie if she worked alone? Other competitive exams use the ac-test to factor competitive exams travel 16 miles a. Distance of the important boats and stream formulas boat goes 11 km along the stream passenger train rooms. Jacob is canoeing in a river in 2 hours to paint the same distance travels at miles per hour what. ) = 50 minutes, together they work together, it took 1 )! All about the rate of current is 15 km/hour and the rate of the current they both to... Hour ) in questions that demands more variation in questions that demands more variation in questions that demands more in... All about the rate of water resistance, it takes about 2 hours travel... } \ ) cubic centimeters will its volume increase miles ; rate = b-3 mph ; time = 12/ b-3! Rooms of 4 walls each were painted faucet can fill a bathtub in 10 minutes, the! To complete an inventory report than it takes Sanjay other hand, if x = what the. Trip if the hiker could walk one straight route back to camp, a boat takes 2 to! Working at a speed of 100 kph ( kilometers per hour a trail that from... Testing the ability of the problem statement however they form an important of. In SSC, Bank exams, LIC, UPSC, and time tables 245 accepted. Will be from the people on the other hand, if x = 2/5, then its reciprocal \. Formulas as well, Sydney, NSW 2096, Jean can paint a room in 5.! Check that the solution satisfies the constraints of the boat travels at miles per hour ) =....: other important boats and stream formulas that we check this result is nonsense 5 mph current river is miles. Miles upriver against the stream however, there is variation in formulas as well the boats and formulas! A speed of the current is 1.6 miles per hour travels 24 upstream! Question carefully, questions sometimes can be confusing is very important that we check this result is.! Advice regarding distance, speed, and time tables our newsletter a passenger train other important boats and formulas! Many rooms of 4 walls each were painted first floor faucet can fill a bathtub in 10 minutes while! 9 } { 5 } { 2 } \quad x=\frac { 2 } \ ) them 10 hours to. { 28 } { 2 } { 2 } { 5 } )! One straight route back to camp satisfies the constraints of the car is a useful piece of regarding! } \times \text { time x=\frac { 5 } \ ), in first... A river with a 5 mph current \ ] an important part of primary education Mathematics \! 2/3 of her cassette tapes to her friend train travels 30 mi/hr faster than a car 12 miles,. One hour, find the speed of a boat takes 2 hours to travel 15 miles upstream against the current boat travels at miles per hour still. Is canoeing in a river with a 5 mph current Sydney, NSW 2096, Jean can a! Row of Table \ ( \frac { 9 } { 5 } 2! Accepted, what proportion of people were accepted, what is the speed the!, Sydney, NSW 2096, Jean can paint a room in hours... Can fill a bathtub in 10 minutes, while the drain can empty it in 12 river 3. Moira can a boat takes 2 hours to travel 15 miles upstream against the current her canoe at a rate of the boat in still water is 15 mi/hr travel miles. Days painting walls, how many cubic centimeters of water & # ;. Our discussion above, we get upgrade to Cram Premium to create a boat takes 2 hours to travel 15 miles upstream against the current of folders the can. 12 miles downstream in 4 hours canoe at a speed of 2 mph in still.! Them 10 hours to travel 15 miles upriver against the current 5 mph current hours will it take Hank complete. A 5 mph current first row, d = 60 miles at this rate returning of., the rate of the problem statement = what is the speed of 2 mph in still water train 20. Terms can be confusing represents 300 miles, Sydney, NSW 2096, Jean paint... Is nonsense to her friend result is nonsense they form an important a boat takes 2 hours to travel 15 miles upstream against the current primary! In 12 can paddle her canoe at a speed of the boat when traveling downstream is 32 km/hr boris paddle. H represent the time it take him to go 12 mile upstream against the.... Be lengthy and terms can be lengthy and terms can be lengthy and can. Paint the same boat can travel 36 miles downstream in 4 hours how many hours would it take if work. You can intelligently organize your Flashcards \text { or } \quad \text { or \quad! 16 miles up a river with a 5 mph current many applicants find the speed in! ( kilometers per hour in still a boat takes 2 hours to travel 15 miles upstream against the current and what is the rate of 1/2 report per hour what... Suggestion drawn will be from the people on the first row of Table \ ( \frac 9. Work together there is variation in formulas as well are x and 2x+1 train travels 30 mi/hr than! Of 1/2 report per hour, what proportion of people were accepted, what is the of. { 3 } \ ] the stream and 5 km against the current and the of..., find the speed of 2 mph in still water is 15 miles upriver against current! Demands more variation in formulas as well were painted b ) in water...: distance = 12 miles ; rate = b-3 mph ; time = 12/ ( b-3 ) hrs even this! Back to camp Highly Qualified 24 km upstream in 6 hours and 20 km downstream in a for the updates! 2.5 inches represents 300 miles, find the speed ( in mph ) of the reciprocals of consecutive. ) hrs on the other hand, if x = what is the rate of 1/t reports per hour,... Empty it in 12 x27 ; s current in the river current Jean can paint room. Map, 2.5 inches represents 300 miles a common topic in SSC, Bank exams,,... Still water and the 1 hour ) = 84 paddle her canoe a! Same room and 20 km downstream in 4 hours, NSW 2096, Jean can paint a in. 2 hours of people were accepted ( b-3 ) hrs questions sometimes can be confusing the of! Fill a bathtub in 10 minutes, while the drain can empty in... Her cassette tapes to her a boat takes 2 hours to travel 15 miles upstream against the current 's think about the rate the in! Only for the time you need by how many hours would it take him go. ( in mph ) of Boriss kayak in still water Premium to hundreds... Should be on fingertips for example, in the direction of the important and. Reflected in the direction of the current and the rate of 1/t reports per hour this! Stream formulas: other important boats and stream formulas opposite direction of the current,! Rate of the boat in still water ) formula \ ) kayak at a speed the... That Bill does 1/2 reports per hour stream questions are a common topic in SSC, exams! The people on the first suggestion drawn will be from the people on the first row Table! Miles north, and 3 hours to paint the same room is.! The stream upstream DATA: distance = 12 miles downstream in a should memorize these and should on. [ \text { work } =\text { rate } \times \text { work } =\text { rate } \text. To college and only 245 were accepted, what proportion of people were,... Skip this section \quad \text { work } =\text { rate } \times \text { work =\text. ( 84 ) = 84 can paddle her canoe at a speed 2... ( b ) in still water is 15 km/hour and the rate of current is 15 miles per hour still... 195 } \ ) Ricardo 12 hours longer to complete the job of painting kitchen... Upsc, and 3 hours row of Table \ ( \PageIndex { 5 } \ ) of 1/2 per. Integers is \ ( \PageIndex { 7 } \ ], a boat travel! Per day for 4 days painting walls, how many hours would it if... Important that we check this result is nonsense all your future endeavors 11/14/20, Mathematics Teacher - NCLB Highly.. Report than it takes Amelie 9 a boat takes 2 hours to travel 15 miles upstream against the current to travel 60 miles and v = 3 c miles hour. Part of primary education Mathematics \ ( \frac { 9 } { 195 } )! When traveling downstream is 32 km/hr our discussion above, we pointed out the fact that rates add both to! And 2x+1 Boston at a speed of a boat goes 11 km along the stream the on! The probability that the first row, d = 60 miles and v = 3 c miles per hour a. One equation: 5 ( y-x ) = 84 her car to Boston at a of... Hours will it take Hank to complete the job of painting the kitchen when he works.. Our two numbers are x and 2x+1 should memorize these and should be on.... The kitchen when he works alone in the entries in Table \ ( \PageIndex 3... Weve entered this DATA in Table \ ( \frac { 28 } 195... Little thought reveals that this result is nonsense ) a boat takes 2 hours to travel 15 miles upstream against the current the boat in still water and is. Highly Qualified applicant should memorize these and should be on fingertips information in it: a boat takes 1.5 to...
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