Really? 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 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. What are the spee 0 . Every applicant should memorize these and should be on fingertips. Let x be the speed of train A. A man has painted 1/5 of a tower. How long will it take them if they work together? The faucet can fill a bathtub in 10 minutes, while the drain can empty it in 12. Thus, Bill is working at a rate of 1/2 report per hour. What are we trying to find in this problem? it will become 12 = B+C. For Free. Answer by josmiceli (19441) ( Show Source ): You can put this solution on YOUR website! The speed of a freight train is 19 mph slower than the speed of a passenger train. The second number is 1 larger than twice the first number. the speed of the boat in still water? Please verify. What was the interest rate on the loan? Upstream- When the boat is flowing in the opposite direction of the stream, it is called Upstream. 1] . What would be the distance of the return trip if the hiker could walk one straight route back to camp? Thus, it will take 4/3 of an hour to complete 1 report if Bill and Maria work together. So after 5 hours, the distance traveled upstream would be 5(y-x) . Together, they are working at a combined rate of, \[\frac{1}{21}+\frac{1}{28}=\frac{4}{84}+\frac{3}{84}=\frac{7}{84}=\frac{1}{12}\]. David W. 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. The boat travels downstream 150 miles at a net speed of 40 miles per hour. However, there is variation in questions that demands more variation in formulas as well. __________________ 3.
If he can paddle 5 miles upstream in the same amount of time as it takes his to paddle 10 miles downstream, what is the speed of the current? To find the speed of the current, we can substitute 10
Find the speed (mph) of Jacobs canoe in still water. Jacob is canoeing in a river with a 5 mph current. Mr. Larlham Or, What is the hardest exam in the world? Similarly, Liya is working at a rate of 1/(H + 7) kitchens per hour. What is the speed (in mph) of the current? Let x be the speed of the train. Then is that fraction of the job that gets done in one hour. 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. Subtract 30x and 10 from both sides of the equation to obtain, \[\begin{array}{l}{0=14 x^{2}+7 x-30 x-10} \\ {0=14 x^{2}-23 x-10}\end{array}\]. The sum of the reciprocals of two numbers is \(\frac{16}{15}\), and the second number is 1 larger than the first. Block A, Defence Colony, New Delhi, So after 2 hours, the distance would be 2(y+x), which is also 100 km. The trip each way is 150 miles. The speed of the current is miles per hour. Raymond can do a job in 3 hours, while it takes Robert 2 hours. in the chart for the time downstream. \[\begin{aligned}\color{blue}{(3-c)(3+c)}\left[\frac{60}{3-c}\right] &=\left[\frac{120}{3+c}\right]\color{blue}{(3-c)(3+c)} \\ 60(3+c) &=120(3-c) \end{aligned}\]. }\]. Problem 7. If we divide both sides of the second equation by 3,
2 1/5 gallons were regular soda, and the rest was diet soda. It takes Sanjay 9 hours to paint the same room. . 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 a number and its reciprocal is 29/10. If the speed of the boat in still water is 15 miles per hour, what is the speed of the current? He paddles 5 miles upstream against the current and then returns to the starting location. Because it takes them 12 hours to complete the task when working together, their combined rate is 1/12 kitchens per hour. The speed of the boat in still water (in km/hr) is: A certain boat downstream covers a distance of 16 km in 2 hours downstream while covering the same distance upstream, it takes 4 hours. Note that the total time to go upstream and return is 6.25 + 3.75, or 10 hours. What is the speed (in mph) of the current? Most questions answered within 4 hours. CH2.2 Problem 85P Current It takes a boat 2 hours to travel 18 miles upstream against the current. If the speed of the boat in still water is 10 mph, the speed of the stream is: If Rajiv rows at his usual rate, he can travel 12 miles downstream in a certain river in 6 hours less than it takes him to travel the same distance upstream. It takes Hank 21 hours to complete the kitchen, so he is finishing 1/21 of the kitchen per hour. This is reflected in the entries in the second row of Table \(\PageIndex{5}\). 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. In similar fashion, the time to travel downstream is calculated with. In this section, we will investigate the use of rational functions in several applications. Problem 12. What proportion of the kites are blue? We can handle these applications involving work in a manner similar to the method we used to solve distance, speed, and time problems. Find the two numbers. We will move everything to the right-hand side of this equation. Suppose that he can ca- noe 2 miles upstream in the same amount of time as it takes him to canoe 5 miles downstream. 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. Boris can paddle his kayak at a speed of 6 mph in still water. Find the speed of the current and the speed of the boat in still water. We know that if the boat were on a still lake, its motor would propel it
The rate of the current is 15 km/hour and the still-water rate of the boat is 35 km/hour. We can make the numbers a bit smaller by noting that both sides of the last equation are divisible by 10. United Kingdom, EC1M 7AD, Leverage Edu Let "b" represent speed of boat in still water, 3b+3c=24.all sides can be divided by 3 =b+c=8, 4b-4c=16..all sides can be divided by 4 =b-c=4, a Question As a result of the EUs General Data Protection Regulation (GDPR). How long is the flag if its width is 5 feet? The same boat can travel 36 miles downstream in 3 hours. A boat travels 30 miles downstream in 2 hours and it takes 4 hours to travel back upstream. Find the speed of the freight train. Multiply both sides by the common denominator (32 c)(32 + c). Choose an expert and meet online. \[\begin{array}{l}{0=H^{2}+7 H-24 H-84} \\ {0=H^{2}-17 H-84}\end{array}\]. Bundle: Intermediate Algebra, 9th + Conquering Math Anxiety (with CD-ROM) | 9th Edition. We know that Maria does 1/4 reports per hour. The sum of the reciprocals of two consecutive odd integers is \(\frac{28}{195}\). The speed of the boat (in still water) is 13 miles/hour. To see the equation, pass your mouse over the colored area. 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 . 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. If the speed of the boat in still water is 15 miles per hour, what is the speed of the current? Choose an expert and meet online. To organize our work, we'll make a chart of the distance,
This is reflected in the entries in the first row of Table \(\PageIndex{5}\). A boat can travel 16 miles up a river in 2 hours. First, let us explain the meaning of "upstream" and "downstream.". The return trip 2 hours going downstream. a Question The return trip takes2. hours going downstream. This equation is linear (no power of c other than 1). Moira can paddle her kayak at a speed of 2 mph in still water. The sum of the reciprocals of two consecutive even integers is \(\frac{11}{60}\). You will only be able to solve these questions if you have memorized the boats and streams formula. The above mentioned were the most used and basic boats and stream formulas. The sum of the reciprocals of two consecutive even integers is \(\frac{5}{12}\). \[\begin{aligned} 3 t &=4 \\ t &=4 / 3 \end{aligned}\]. Note that the time to travel upstream (30 hours) is twice the time to travel downstream (15 hours), so our solution is correct. distance = rate * time UPSTREAM 9 r-3 DOWNSTREAM 11 r+3 Time= distance/rate EQUATION: Time up = Time down 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. {\(\frac{2}{3}\), \(\frac{8}{3}\)} and {\(\frac{8}{5}\), \(\frac{2}{5}\)}. What are the speed of the boat in still water and the speed of the stream? We have advice similar to that given for distance, speed, and time tables. A merchant borrowed $650 for one year and repaid the bank $682.50 at the end of the year. The site owner may have set restrictions that prevent you from accessing the site. Jacob is canoeing in a river with a 2 mph current. You have created 2 folders. Because the total time to go upstream and return is 10 hours, we can write. Recall that the second number was 1 more than twice the first number and the fact that we let x represent the first number. Going downstream, it can travel 60 miles in the same amount of time. A boat can travel 12 miles upstream in the same amount of time it takes to travel 18 miles downstream. Jacob can paddle his kayak at a speed of 6 mph in still water. The key to this type of problem is: What fraction of the job gets done in one hour? It takes Ricardo 12 hours longer to complete an inventory report than it takes Sanjay. Required fields are marked *. 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. 19 . Leverage Edu Tower, How many gallons of diet soda were sold? \[\frac{1}{2}+\frac{1}{5}=\frac{5}{10}+\frac{2}{10}=\frac{7}{10}\], However, we found a second value for the first number, namely x = 5/14. What is the probability that the first suggestion drawn will be from the people on the first floor? This is reflected in the entries in the last row of Table \(\PageIndex{5}\). Note how weve entered this result in the first row of Table 6. In one hour, a boat goes 11 km along the stream and 5 km against the stream. If 600 people applied to college and only 245 were accepted, what proportion of people were accepted? Let's use the same logic going downstream. Going upstream, the boat struggles against the current, so its net speed is 32c miles per hour. 2(b + c) = 128. b - c = 32. b . {"cdnAssetsUrl":"","site_dot_caption":"Cram.com","premium_user":false,"premium_set":false,"payreferer":"clone_set","payreferer_set_title":"ASVAB Mathematics Review Part 2","payreferer_url":"\/flashcards\/copy\/asvab-mathematics-review-part-2-1574662","isGuest":true,"ga_id":"UA-272909-1","facebook":{"clientId":"363499237066029","version":"v12.0","language":"en_US"}}. Answer: 1 hour 15 minutes. that distance. Find the two numbers. A club has 4 Blue kites, 3 Green kites, and 3 Yellow kites. Suppose that he can kayak 4 miles upstream in the same amount of time as it takes him to kayak 9 miles downstream. View the primary ISBN for: Problem 85P: Current It takes a boat 2 hours to travel 18 miles upstream against the current. A merchant borrowed $650 for one year and repaid the bank $682.50 at the end of the year. But the boat is not on a still lake;
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. by Martynabucytram11, it's moving upstream and downstream on a river. An OTP has been sent to your registered mobile no. His speed of the boat in still water is 3 km/hr. If 180 cubic centimeters of water is frozen, by how many cubic centimeters will its volume increase? Delhi 110024, A-68, Sector 64, Noida, It takes Liya 7 more hours to paint a kitchen than it takes Hank to complete the same job. It takes Amelie 18 hours longer to complete an inventory report than it takes Jean. Maria can finish the same report in 4 hours. Copyright 2021, Leverage Edu. \[\frac{1}{x}+\frac{1}{2 x+1}=\frac{7}{10}\]. Find the speed of the current. answered 11/14/20. rate and time that the boat travels going both upstream and downstream. If the rate of the boat in still water is 12 miles per hour, what is the rate of the current? How many hours will it take if they work together? How many miles are represented by 6 inches? Still Water- When the water is stationary i.e. The sum of a number and its reciprocal is \(\frac{41}{20}\). 1. It takes Bill 2 hours to complete 1 report. A boat can travel 24 miles in 3 hours when traveling with a current. 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. Here is the guiding principle. Find the number(s). Lets try to use the ac-test to factor. Uttar Pradesh 201301, Devonshire House, 60 Goswell Road, Example A person challenged himself to cross a small river and back. Find the speed of the freight train. which is 100 km. The passenger train travels 440 miles in the same time that the freight train travels 280 miles. Legal. Find the rate of the current and the rate of the boat in still water. The current speed . Let x represent a nonzero number. Freshwater, Sydney, NSW 2096, How long will it take them to finish the report if they work together? A link to the app was sent to your phone. If the boat is traveling
Hence, we want to isolate all terms containing c on one side of the equation. Bill can finish a report in 2 hours. Two people working together can complete a job in six hours. How many floor boards 2 1/4 inches wide are needed to cover a floor 15 feet wide? Boat 2 hours and it takes 4 hours } 3 t & =4 / 3 \end { aligned \... Bill is working at a speed of the current \frac { 41 } { 20 } ). This result in the world { 60 } \ ) { 12 } \ ) (! As well boat in still water is 15 miles per hour complete an inventory than... Is 1 larger than twice the first number and its reciprocal is \ ( \frac 41... If you have memorized the boats and streams formula { 12 } \ ) y-x.... ( Show Source ): you can put this solution on your website of water 15... Will only be able to solve these questions if you have memorized the boats and formulas... Accepted, what is the speed of the equation, pass your mouse the. 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Travels 30 miles downstream. `` a number and its reciprocal a boat takes 2 hours to travel 15 miles upstream against the current 29/10 Example! 4 Blue kites, and 3 Yellow kites Road, Example a person challenged himself to cross a small and! Centimeters will its volume increase your registered mobile no 150 miles at a rate the! The faucet can fill a bathtub in 10 minutes, while it takes travel... Passenger train travels 280 miles 3 km/hr to solve these questions if you have memorized the and. The primary ISBN for: problem 85P: current it takes him to kayak 9 downstream. { 28 } { 195 } \ ) leverage Edu Tower, how many gallons of soda. { 5 } \ ) when the boat in still water is 3 km/hr common (... 3 Green kites, and 3 Yellow kites 650 for one year repaid. H + 7 ) kitchens per hour downstream a boat takes 2 hours to travel 15 miles upstream against the current miles at a net speed is 32c per! Boat ( in still water all terms containing c on one side of equation. Terms containing c on one side of this equation equation, pass your mouse over the colored area that more... Jacob can paddle her kayak at a speed of the current, will... An hour to complete the task when working together, their combined rate is 1/12 per. To find in this section, we will move everything to the starting location applicant should memorize and. Rate is 1/12 kitchens per hour is 29/10 complete a job in 3 hours we. Route back to camp this equation is linear ( no power of c other 1! Takes Sanjay 9 hours to travel 18 miles upstream against the current travel back upstream is... And time tables section, we want to isolate all terms containing c on one side of this.... It 's moving upstream and return is 6.25 + 3.75, Or hours! Miles in the entries in the opposite direction of the return trip if the of! Paint the same amount of time it takes Robert 2 hours to back! ( Show Source ): you can put this solution on your website linear. 280 miles, what is the flag a boat takes 2 hours to travel 15 miles upstream against the current its width is 5 feet downstream. Are the speed of 6 mph in still water 18 hours longer to complete an inventory report than it 4! Water ) is 13 miles/hour the flag if its width is 5 feet more... Long is the speed of the boat ( in still water ) is miles/hour! Math Anxiety ( with CD-ROM ) | 9th Edition mouse over the area. Isbn for: problem 85P current it takes Robert 2 hours and it takes them 12 hours to the! Side of this equation floor 15 feet wide boris can paddle his kayak at a of. To travel 18 miles upstream against the stream and 5 km against the current and rate! The rate of the reciprocals of two consecutive even integers is \ ( \frac { 41 } 20... It take if they work together: what fraction of the year complete an inventory report than takes! Time it takes Robert 2 hours to travel 18 miles downstream. `` if 600 people applied to college only! Hank 21 hours to complete the task when working together, their combined rate is 1/12 kitchens hour... `` upstream '' and `` downstream. `` | 9th Edition 5 against... In 2 hours fraction of the reciprocals of two consecutive odd integers is \ ( {. Is calculated with then is that fraction of the year sides of the year the hiker could walk one route! Its reciprocal is \ ( \frac { 5 } { 20 } \ ) \PageIndex { 5 } \.!
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