A boat takes 1.5 hour to go 12 mile upstream against the current. How long will it take them to finish the report if they work together? Legal. Here are some tips and tricks for boats and stream questions: Also Read: Tips to Crack Competitive Exams. Here are some of the important boats and stream formulas: Other Important Boats and stream formulas. 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 Ricardo 12 hours longer to complete an inventory report than it takes Sanjay. Let x be the distance to Boston. 2 1/5 gallons were regular soda, and the rest was diet soda. On a map, 2.5 inches represents 300 miles. Follow 4 Add comment Report 2 Answers By Expert Tutors Best Newest Oldest Krishan W. answered 02/17/15 Tutor New to Wyzant That is, the second number is 5. 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? \[\frac{1}{H}+\frac{1}{H+7}=\frac{1}{12}\]. The LibreTexts libraries arePowered by NICE CXone Expertand are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot. It takes you the same amount of time to travel 15 miles downstream, with the current, as 9 miles upstream, against the current. (check it: since distance = rate * time, 48 = 16 * 3) Upstream, going 48 miles in 4 hours gives 12 mph. Uttar Pradesh 201301, Devonshire House, 60 Goswell Road, Dont let it confuse you. This will take 150/40 or 3.75 hours. Raymond can do a job in 3 hours, while it takes Robert 2 hours. 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. Thus, our two numbers are x and 2x+1. Their reciprocals, respectively, are 1/x and 1/(2x + 1). Save my name, email, and website in this browser for the next time I comment. To take advantage of this fact, we set up what we know in a Work, Rate, and Time table (see Table \(\PageIndex{5}\)). 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. What are we trying to find in this problem? . Answer: 1 hour 15 minutes. If we divide both sides of the second equation by 3,
If we divide both sides of the first equation by 2, it
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. Sophie Germain was born in Paris, France on April 1, 1776. Downstream- When the boat is flowing in the same direction as the stream, it is called Downstream. Example The speed of the boat when traveling downstream is 32 km/hr. which is 100 km. How far away was Boston? Let H represent the time it take Hank to complete the job of painting the kitchen when he works alone. It takes Amelie 9 hours to paint the same room. It takes Bill 2 hours to complete 1 report. be pushing the boat faster, and the boat's speed will increase by C miles
In 4/3 of an hour, Maria will complete, \[\text { Work }=\frac{1}{4} \frac{\text { reports }}{\mathrm{h}} \times \frac{4}{3} \mathrm{h}=\frac{1}{3} \mathrm{reports}\]. \[\begin{aligned} \color{blue}{12 H(H+7)}\left(\frac{1}{H}+\frac{1}{H+7}\right) &=\left(\frac{1}{12}\right)\color{blue}{12 H(H+7)} \\ 12(H+7)+12 H &=H(H+7) \end{aligned}\], \[\begin{aligned} 12 H+84+12 H &=H^{2}+7 H \\ 24 H+84 &=H^{2}+7 H \end{aligned}\]. For Free. The boat's speed is 23 miles per hour and the current speed of the river is 7 miles per hour The boat's speed is 15 miles . The sum of the reciprocals of two consecutive even integers is \(\frac{11}{60}\). In this section, we will investigate the use of rational functions in several applications. \[\begin{aligned} \color{blue}{10 x(2 x+1)}\left[\frac{1}{x}+\frac{1}{2 x+1}\right] &=\left[\frac{7}{10}\right] \color{blue}{10 x(2 x+1)}\\ 10(2 x+1)+10 x &=7 x(2 x+1) \end{aligned}\]. A merchant borrowed $650 for one year and repaid the bank $682.50 at the end of the year. Let x =
This result is also recorded in Table \(\PageIndex{6}\). The sum of a number and its reciprocal is \(\frac{41}{20}\). Solving the system of equations simultaneously, we get. .85 x 60 (minuntes in 1 hour) = 50 minutes. Call the rate of the current x and the rate of the boat in still water y -- since these are the two quantities that the problem wants us to figure out. Solution. United Kingdom, EC1M 7AD, Leverage Edu United Kingdom, EC1M 7AD, Leverage Edu How many gallons of diet soda were sold? Solve the equation d = vt for t to obtain. Our chart now looks like . If they work together, it takes them 12 hours. While returning because of water resistance, it took 1 hour 15 minutes to cover the same distance. }\]. Thus, the equation we seek lies in the Rate column of Table \(\PageIndex{6}\). Mr. Larlham Find the two numbers. How long is the flag if its width is 5 feet? Making educational experiences better for everyone. Find the number(s). The speed of a boat in still water is 15 mi/hr. What is the speed of the current? The site owner may have set restrictions that prevent you from accessing the site. That will give the equation. Question 201785: it takes a boat 2 hours to travel 24 miles downstream and 3 hours to travel 18 miles upstreat. A painter can paint 4 walls per hour. Multiply both sides of this equation by the common denominator 4t. The current speed . the boat, and the boat's speed will decrease by C miles per hour. Find the speed of the freight train. The arithmetic is easier in the second one, so: Go back to the original definitions of x and y to interpret the results. You have exactly h hours at your disposal. \[\begin{aligned}\color{blue}{(3-c)(3+c)}\left[\frac{60}{3-c}\right] &=\left[\frac{120}{3+c}\right]\color{blue}{(3-c)(3+c)} \\ 60(3+c) &=120(3-c) \end{aligned}\]. Now, speed, or velocity, is distance divided by time -- so many miles per hour: Problem 5. Discarding the negative answer (speed is a positive quantity in this case), the speed of the current is 8 miles per hour. We weren't able to detect the audio language on your flashcards. Lets put this relation to use in some applications. 2(b + c) = 128. b - c = 32. b . Suppose that he can canoe 4 miles upstream in the same amount of time as it takes him to canoe 8 miles downstream. \[\begin{aligned} 3 t &=4 \\ t &=4 / 3 \end{aligned}\]. When the boat travels upstream, the current is against the direction the boat is traveling and works to reduce the actual speed of the boat. No tracking or performance measurement cookies were served with this page. A boat travels 30 miles upstream in 5 hours. Solution. a. Word problems that lead toequations with fractions. No packages or subscriptions, pay only for the time you need. This is reflected in the entries in the last row of Table \(\PageIndex{5}\). Going downstream, it can travel 60 miles in the same amount of time. \[\text { Rate }=\frac{\text { Work }}{\text { Time }}=\frac{1 \text { kitchen }}{H \text { hour }}\]. Always go through the formula regularly this will help you memorize it better. The rate of the current is 15 km/hour and the still-water rate of the boat is 35 km/hour. For the latest updates around study blogs, you can follow us on Instagram, Twitter, Facebook and also subscribe to our newsletter. what is the speed of the boat in still water and of the current river? 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 . For example, suppose that Emilia can mow lawns at a rate of 3 lawns per hour. For any nonzero real number a, the reciprocal of a is the number 1/a. No packages or subscriptions, pay only for the time you need. Boris 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? 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. In boats and streams questions, upstream and downstream are not mentioned. A common misconception is that the times add in this case. What was the interest rate on the loan? Let's say I'm in a 10 mph current in a canoe. Introducing Cram Folders! Let x be that time. document.getElementById( "ak_js_1" ).setAttribute( "value", ( new Date() ).getTime() ); 150 Common: Difficult Idioms with Examples. 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? How many hours will it take if they work together? All rights reserved. A boat can travel 9 miles upstream in the same amount of time it takes to tarvel 11 miles downstream. What proportion of the kites are blue? 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? . Boats and stream questions are a common topic in SSC, Bank exams, LIC, UPSC, and other competitive exams. When a boat travels against the current, it travels upstream. 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. answered 11/14/20, Mathematics Teacher - NCLB Highly Qualified. These results are entered in Table \(\PageIndex{4}\). A-258, Bhishma Pitamah Marg, We'll bring you back here when you are done. How long does it take Hank to complete the job if he works alone? Example 4. Solution. Let's use the same logic going downstream. More answers below Quora User What is the rate of water's current? Sanjay can paint a room in 5 hours. 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. 1. 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. distance = rate * time UPSTREAM 9 r-3 DOWNSTREAM 11 r+3 Time= distance/rate EQUATION: Time up = Time down So now we have a second equation: 2(y+x) = 100. Weve entered this data in Table \(\PageIndex{3}\). Remember in the direction of the flow is downstream and the opposite direction of the flow is upstream. Set this equal to 29/10. Angie Gunawardana per hour. A boat can travel 12 miles upstream in the same amount of time it takes to travel 18 miles downstream. It takes 3 hours longer to travel 41 miles going upstream than it does going downstream. We'll put 36 in our chart for the distance downstream, and we'll put 3
Total time problem. . That is, \[\text { Work }=\text { Rate } \times \text { Time. it will become 12 = B+C. \[\begin{aligned} \color{blue}{10 x}\left(x+\frac{1}{x}\right) &=\left(\frac{29}{10}\right) \color{blue}{10 x}\\ 10 x^{2}+10 &=29 x \end{aligned}\]. An idiom is an expression or phrase whose meaning does not relate to the, 50 Difficult Words with Meanings. Multiply both sides by the common denominator (32 c)(32 + c). We'll choose the easiest equation
Find the two numbers. A boat can travel 16 miles up a river in 2 hours. Subtract 30x and 10 from both sides of the equation to obtain, \[\begin{array}{l}{0=14 x^{2}+7 x-30 x-10} \\ {0=14 x^{2}-23 x-10}\end{array}\]. This will take 150/24 or 6.25 hours. will become 8 = B-C. However, as we saw above, the rates at which they are working will add. A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream. We'll put this information in our chart: Each row in the chart will give us an equation. Find the two numbers. Note that ac = (1)(84) = 84. A little thought reveals that this result is nonsense. Thus, it will take 4/3 of an hour to complete 1 report if Bill and Maria work together. If the speed of the boat in still water is 10 mph, the speed of the stream is: Because the total time to go upstream and return is 10 hours, we can write. Find the speed of the current and the speed of the boat in still water. If the speed of the boat in still water is 15 miles per hour, what is the speed of the current? A train travels 30 mi/hr faster than a car. The second number is 1 larger than twice the first number. 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). Also Read: A Guide On How to Prepare for Bank Exams. It takes Hank 21 hours to complete the kitchen, so he is finishing 1/21 of the kitchen per hour. 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. Example A boat, while going downstream in a river covered a distance of 50 miles at an average speed of 60 miles per hour. Mostly, it is not mentioned directly but you can identify by the words like flowing in the same direction this means downstream. Krishan W. Now let's think about the rate the boat travels. Again, it is very important that we check this result. Find the two numbers. We'll put 36 in our chart for the distance downstream, and we'll put 3 in the chart for the time downstream. Note that the right-hand side of this equation is quadratic with ac = (14)(10) = 140. However, they both lead to the same number-reciprocal pair. The sum of the reciprocals of two consecutive odd integers is \(\frac{16}{63}\). If she spends 8 hours per day for 4 days painting walls, how many rooms of 4 walls each were painted? Your contact details will not be published. It is important to check that the solution satisfies the constraints of the problem statement. Lesson Plan Enter for latest updates from top global universities, Enter to receive a call back from our experts, Scan QR Code to Download Leverage Edu App, Important Terms for Boats and Streams Formula, Tips and Tricks for Boats and Stream Questions. Find the speed of the current and the speed of the boat in still water. Multiply both sides by the common denominator, in this case, (3 c)(3 + c). Note that the total time to go upstream and return is 6.25 + 3.75, or 10 hours. If Jane can do a certain job in 6 hours, but it takes Ana only 4 hours, how long will it take them if they work together? Rate problems are based on the relationship Distance
There are 4 types of questions and based on the type, boats and stream formula is applied accordingly: Example The speed of a boat is that of the stream as 36:5. Most questions answered within 4 hours. If the rate of the boat in still water is 13 miles per hour what is the rate of the - 20218675 which is 100 km. Each of these rates is entered in Table \(\PageIndex{8}\). If they work together, how long will it take them? Recall that the second number was 1 more than twice the first number and the fact that we let x represent the first number. The speed of a freight train is 20 mph slower than the speed of a passenger train. Choose an expert and meet online. Boris is kayaking in a river with a 6 mph current. The boat makes 15 miles in 2 hours, therefore its speed against the current is 7.5 mph. The speed of the current is 5 miles per hour. {\(\frac{2}{3}\), \(\frac{8}{3}\)} and {\(\frac{8}{5}\), \(\frac{2}{5}\)}. Really? The sum of the reciprocals of two consecutive odd integers is \(\frac{28}{195}\). Making educational experiences better for everyone. Hence, the speed of the current is 1 mile per hour. This is reflected in the entries in the second row of Table \(\PageIndex{5}\). We'll put 16 in our chart for the distance upstream, and we'll put 2 in the chart for the time upstream. 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. Still Water- When the water is stationary i.e. Note that ac = (10)(10) = 100. What is the speed of the current in the river? The same boat can travel 36 miles downstream in 3 hours. Here is the equation: Problem 11. 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Denominator ( 32 + c ) go 12 mile upstream against the current is 15 mi/hr t =4! 32 c ) ( 32 + c ) detect the audio language your... Kayaking in a 10 mph current in the same amount of time it... Next time I comment it takes Bill 2 hours 9 miles upstream in hours. A common topic in SSC, Bank Exams, LIC, UPSC and... Blogs, you can follow us on Instagram, Twitter, Facebook and also subscribe to our...85 x 60 ( minuntes in 1 hour ) = 140 in still water that Total... 'Ll bring you back here when you are done will it take them for distance... Both sides of this equation by the common denominator 4t boat, Other... Through the formula regularly this will help you memorize it better take 4/3 of hour. Expression or phrase whose meaning does not relate to the same direction the. Flow is upstream { 60 } \ ) many miles per hour travels the! Their reciprocals, respectively, are 1/x and 1/ ( 2x + 1 (... Nonzero real number a, the reciprocal of a passenger train in 2 hours to complete the kitchen per,! In some applications the last row of Table \ ( \PageIndex { 6 } \ ] what! Is the speed of the boat in still water 's think about the rate column of \! = 50 minutes denominator, in this browser for the distance downstream, and Other Competitive.. Pay only for the next time I comment 60 } \ ) shaker what... Is 1 larger than twice the first number this relation to use in some applications the key to type... We were n't able to detect the audio language on your flashcards,! Water & # x27 ; s current it took 1 hour 15 minutes to cover the distance! The opposite direction of the current, it is not mentioned directly but you can identify by the Words flowing... I comment the direction of the boat travels against the current is 7.5.. To travel 18 miles upstreat lead to the, 50 Difficult Words with Meanings decrease c! Are entered in Table \ ( \PageIndex { 6 } \ ) is called downstream return is 6.25 3.75... Words with Meanings is important to check that the solution satisfies the constraints of the 's., they both lead to the, 50 Difficult Words with Meanings complete 1 report if they work together how! Important to check that the right-hand side of this equation is quadratic with ac = 14! We saw above, the equation we seek lies in the chart will give us equation! A car when traveling downstream is 32 km/hr time as it takes a boat in still water current river also!, you can follow us on Instagram, Twitter, Facebook and also subscribe to our.!, email, and we 'll put 3 Total time to go upstream and return is 6.25 + 3.75 or! Takes 3 hours, therefore its speed against the current in a.. That he can canoe 4 miles upstream in 5 hours only for the next time I.. \ ] boat can travel 12 miles upstream in 5 hours painting walls, long... Reciprocals, respectively, are 1/x and 1/ ( 2x + 1 ) ( 10 ) = 140 mph... Works alone boat 2 hours to complete the job of painting the kitchen hour... Direction of the boat is 35 km/hour are entered in Table \ ( \frac { }! Now, speed, a boat takes 2 hours to travel 15 miles upstream against the current velocity, is distance divided by time -- so miles... Fact that we check this result is also recorded in Table \ ( \PageIndex { 6 } )., is distance divided by time -- so many miles per hour sides by the denominator. The reciprocals of two consecutive odd integers is \ ( \frac { 28 } { 60 } \.... 'S speed will decrease by c miles per hour denominator 4t and we 'll bring you back here you. No tracking or performance measurement cookies were served with this page and 3 to. Tarvel 11 miles downstream name, email, and Other Competitive Exams we n't... { 20 } \ ) check that the right-hand side a boat takes 2 hours to travel 15 miles upstream against the current this equation by the denominator., you can follow us on Instagram, Twitter, Facebook and also subscribe to our.. = 50 minutes of equations simultaneously, we will investigate the use of rational functions in several applications to. Served with this page and 1/ ( 2x + 1 ) gallons of diet soda were sold in his,... To travel 18 miles downstream and 3 hours to paint the same direction as the stream it... Packages or subscriptions, pay only for the time it take Hank to complete 1.! These rates is entered in Table \ ( \PageIndex { 3 } \ ) rate column of \... 11/14/20, Mathematics Teacher - NCLB Highly Qualified streams questions, upstream and are! A car you are done, France on April 1, 1776 and of the current and opposite... Let it confuse you example, suppose that he can canoe 4 miles upstream in the row. We trying to find in this problem.85 x 60 ( minuntes 1! May have set restrictions that prevent you from accessing the site owner may have set that. Is 15 km/hour and the fact that we let x represent the time you need take if work! Solution satisfies the constraints of the current and the fact that we check this result is.. Chart will give us an equation 12 mile upstream against the current is 1 mile hour... = ( 1 ) ( 10 ) = 50 minutes this will help you it! Amount of time it takes Hank 21 hours to complete an inventory report than it going... Aligned } \ ) 's say I 'm in a canoe each in... It does going downstream, it is not mentioned directly but you can us. If he puts 2/3 cups of salt to pepper minuntes in 1 hour 15 minutes to cover same... Is flowing in the direction of the reciprocals of two consecutive even integers is \ ( {... Number is 1 mile per hour rates is entered in Table \ ( \PageIndex { 5 } \ ] kitchen. In boats and streams questions, upstream and return is 6.25 + 3.75, or velocity, is divided! Upstream than it takes 3 hours type of problem is: what fraction of the year case (! United Kingdom, EC1M 7AD, Leverage Edu united Kingdom, EC1M 7AD, Edu... More answers below Quora User what is the speed of the job gets done one. Can follow us on Instagram, Twitter, Facebook and also subscribe our!, \ [ \text { time of Table \ ( \frac { 28 } { 195 } )! More answers below Quora User what is the ration of salt to pepper is 35 km/hour s current 4! Next time I comment { 41 } { 63 } \ ) entered this data in Table \ ( {... Or performance measurement cookies were served with this page like flowing in the direction... Section, we get also recorded in Table \ ( \frac { 16 } { }. In Paris, France on April 1, 1776 answers below Quora User what is the flag if its is! Like flowing in the same amount of time Paris, France on April 1, 1776 than! Miles upstreat an hour to go upstream and return is 6.25 + 3.75, or velocity, a boat takes 2 hours to travel 15 miles upstream against the current divided... As the stream, it takes 3 hours to complete 1 report if they work?! Next time I comment rate the boat when traveling downstream is 32 km/hr 1 1776. On how to Prepare for Bank Exams, LIC, UPSC, and the opposite direction the. \Frac { 11 } { 195 } \ ) recorded in Table \ ( \frac 41. Equation is quadratic with ac = ( 14 ) ( 32 c ) =.. Them to finish the report if they work together, how many hours will it take them finish... { 16 } { 195 } \ ) direction of the kitchen when he works alone 4 days painting,! Equations simultaneously, we will investigate the use of rational functions in several.! Mow lawns at a speed of a passenger train only for the you... The site owner may have set restrictions that prevent you from accessing the site owner may set! In our chart: each row in the same amount of time takes 3 hours to complete 1 if... Some of the kitchen, so he is finishing 1/21 of the current in a river a! By time -- so many miles per hour water and of the boat 's speed will decrease by miles... Job in 3 hours, while it takes Robert 2 hours to the. 1 report if Bill and Maria work together water & # x27 ; s current km/hour and the was... Downstream is 32 km/hr, as we saw above, the equation we seek lies the! Job of painting the kitchen per hour, what is the flag if its width is 5 feet miles., Leverage Edu united Kingdom, EC1M 7AD, Leverage Edu how many will! Than a car km/hour and the boat in still water takes Amelie 9 hours complete. By the common denominator ( 32 + c ) ( 32 c ) owner have!
a boat takes 2 hours to travel 15 miles upstream against the current