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a boat takes 2 hours to travel 15 miles upstream against the current

10 de março de 2023

The chart will give us the information about distance, rate and time that 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. How many hours will it take if they work together? where d represents the distance traveled, v represents the speed, and t represents the time of travel. A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream. \[x=\frac{5}{2} \quad \text { or } \quad x=\frac{2}{5}\]. Find the number(s). This leads to the entries in Table \(\PageIndex{7}\). Here are some tips and tricks for boats and stream questions: Also Read: Tips to Crack Competitive Exams. So now we have a second equation: 2(y+x) = 100. Therefore, The rate of current is, Hence, The required rate of current is 1.6. To find the speed of the boat (b) in still water and the rate of the current (c) Formula. Sophie Germain was born in Paris, France on April 1, 1776. We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. The site owner may have set restrictions that prevent you from accessing the site. 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. The speed of the boat as it goes downstream (with the current) will be 4 miles per hour. }\]. A boat takes 1.5 hour to go 12 mile upstream against the current. If the speed of the boat in still water is 15 miles per hour, what is the speed of the current? What is (check it: since distance = rate * time, 48 = 16 * 3) Upstream, going 48 miles in 4 hours gives 12 mph. The total time of the trip is 9 hours. The boat travels at miles per hour in still water. 3 . It takes Liya 7 more hours to paint a kitchen than it takes Hank to complete the same job. If they work together, it takes them 8 hours. She paddles 3 miles upstream against the current and then returns to the starting location. Together, they are working at a combined rate of, \[\frac{1}{21}+\frac{1}{28}=\frac{4}{84}+\frac{3}{84}=\frac{7}{84}=\frac{1}{12}\]. 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 second number is 1 larger than twice the first number. that distance. The sum of a number and twice its reciprocal is \(\frac{17}{6}\). How long it takes the faster one. You will only be able to solve these questions if you have memorized the boats and streams formula. Raymond can do a job in 3 hours, while it takes Robert 2 hours. He paddles 5 miles upstream against the current and then returns to the starting location. answered 02/17/15. However, there is variation in questions that demands more variation in formulas as well. Let H represent the time it take Hank to complete the job of painting the kitchen when he works alone. our information in it: A boat can travel 16 miles up a river in 2 hours. not flowing then the speed of water is zero. 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. What are we trying to find in this problem? Note that the time to travel upstream (30 hours) is twice the time to travel downstream (15 hours), so our solution is correct. 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. When the boat travels downstream, then the actual speed of the boat is its speed in still water increased by the speed of the current. Suppose that he can kayak 4 miles upstream in the same amount of time as it takes him to kayak 9 miles downstream. You have exactly h hours at your disposal. That is, if x = 5/2, then its reciprocal is 2/5. How tall is the tower? Then. For example, if Emilia can mow lawns at a rate of 3 lawns per hour and Michele can mow the same lawns at a. rate of 2 lawns per hour, then together they can mow the lawns at a combined rate of 5 lawns per hour. Solution : Speed of the boat in still water = 30 km/hr. We know that if the boat were on a still lake, its motor would propel it Jean can paint a room in 4 hours. Accessibility StatementFor more information contact us atinfo@libretexts.orgor check out our status page at https://status.libretexts.org. Defence Colony, New Delhi, A speedboat can travel 32 miles per hour in still water. If the current of the river is 3miles per hour, complete the chart below and use it to find the speed of the boat in still water. answered 02/17/15, Olubunmi B. We can handle these applications involving work in a manner similar to the method we used to solve distance, speed, and time problems. Thus, Bill is working at a rate of 1/2 report per hour. Against the same current, it can travel only 16 miles in 4 hours. Next Lesson: Radicals: Rational and irrational numbers. On the return trip, the boat benefits from the current, so its net speed on the return trip is 32 + c miles per hour. Note that we simply invert the number 3 to obtain its reciprocal 1/3. 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? Example 4. How long will it take them to finish the report if they work together? 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. Hence, the sum of x and its reciprocal is represented by the rational expression x + 1/x. Let t represent the time it takes them to complete 1 report if they work together. Find the speed of the freight train. Please upgrade to Cram Premium to create hundreds of folders! Find the two numbers. Their reciprocals, respectively, are 1/x and 1/(2x + 1). Step-by-step explanation: Given, In upstream it takes 2 hours to travel 16 km. The reciprocal of x is 1/x. Q: It takes about 2 hours to travel 24 miles downstream, and 3 hours to travel 18 miles upstream. The speed of the boat in still water is 3 miles per hour. Jon P. He calculated the speed of the river that day as 1 km/hr. 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 . Example 5. Because it takes Liya 7 more hours than it takes Hank, let H + 7 represent the time it takes Liya to paint the kitchen when she works alone. The sum of the reciprocals of two consecutive odd integers is \(\frac{16}{63}\). If the boat is traveling When we developed the Equations of Motion in the chapter on quadratic functions, we showed that if an object moves with constant speed, then the distance traveled is given by the formula. Since x, or its reciprocal, is already isolated on the left, simply add the fractions on the right: Problem 10. 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. However, they both lead to the same number-reciprocal pair. Block A, Defence Colony, New Delhi, That is, Maria will complete 1/3 of a report. Total time problem. Let's say I'm in a 10 mph current in a canoe. Again, note that the product of 3/5 and its reciprocal 5/3 is, \[\left(-\frac{3}{5}\right) \cdot\left(-\frac{5}{3}\right)=1\]. 3.17.8: Applications of Rational Functions is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts. . This will take 150/24 or 6.25 hours. End-to-end support for your study abroad journey. We'll put 16 in our chart for the distance upstream, and we'll put 2 in Lesson Plan Find the number(s). A-258, Bhishma Pitamah Marg, Block A, Example A person challenged himself to cross a small river and back. }\], A second important concept is the fact that rates add. 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. 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? Find the speed of the current. 19 . 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. The speed of the current is miles per hour. The same boat can travel 36 miles downstream in 3 hours. Break up the middle term of the quadratic trinomial using this pair, then factor by grouping. If they work together, how long will it take them? What is the rate of the boat in still water and what is the rate of the current? Find the two numbers. How much time will it take to come back? 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. 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? 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An OTP has been sent to your registered mobile no. Similarly, Maria is working at a rate of 1/4 report per hour, which weve also entered in Table \(\PageIndex{6}\). It takes Amelie 18 hours longer to complete an inventory report than it takes Jean. David W. Train A has a speed 15 mi/hr greater than train B. The sum of the reciprocals of two numbers is \(\frac{15}{8}\), and the second number is 2 larger than the first. 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. it's moving upstream and downstream on a river. Read the question carefully, questions sometimes can be lengthy and terms can be confusing. He started at the tower's base and is now 35 feet above the ground. Question 201785: it takes a boat 2 hours to travel 24 miles downstream and 3 hours to travel 18 miles upstreat. It takes Sanjay 7 hours to paint the same room. A student gave 2/3 of her cassette tapes to her friend. If one of them works twice as fast as the other, how long would it take the faster one working alone? If they work together, it takes them 3 hours. If 180 cubic centimeters of water is frozen, by how many cubic centimeters will its volume increase? Answer: 1 hour 15 minutes. A boat can travel 16 miles up a river in 2 hours. Find the speed (mph) of Jacobs canoe in still water. Rate problems are based on the relationship Distance How long will it take them if they work together? of two equations to solve. so we have 2 equations which must be solved . No packages or subscriptions, pay only for the time you need. Find the speed of the freight train. }\]. If train A travels 150 miles in the same time train B travels 120 miles, what are the speeds of the two trains? How do we find the two equations we need? 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? A boat takes 1.5 hour to go 12 mile upstream against the current. We start by recalling the definition of the reciprocal of a number. Find the speed (mph) of Boriss kayak in still water. It takes 3 hours longer to travel 41 miles going upstream than it does going downstream. 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. View this answer View a sample solution Step 1 of 3 Step 2 of 3 Step 3 of 3 Back to top For the latest updates around study blogs, you can follow us on Instagram, Twitter, Facebook and also subscribe to our newsletter. Weve also added this entry to the time column in Table \(\PageIndex{2}\). Find the two numbers. What is the speed of the boat in still water? Note that, \[\frac{5}{2}+\frac{2}{5}=\frac{25}{10}+\frac{4}{10}=\frac{29}{10}\]. Problem 7. A train travels 30 mi/hr faster than a car. Therefore, the sum of their reciprocals can be represented by the rational expression 1/x + 1/(2x + 1). Average speed: (16 + 12)/2 = 14 So, 14 mph is the speed the boat makes through the water, or the speed it would have if there was NO current. For example, in the first row, d = 60 miles and v = 3 c miles per hour. Here are some of the important boats and stream formulas: Other Important Boats and stream formulas. Then the speed of the car is Your contact details will not be published. Water volume increases 9% when it freezes. by Martynabucytram11, Because work, rate, and time are related by the equation \[\text { Work }=\text { Rate } \times \text { Time }\] whenever you have two boxes in a row completed, the third box in that row can be calculated by means of the relation Work \(=\) Rate \(\times\) Time. Note that the right-hand side of this equation is quadratic with ac = (14)(10) = 140. After 6 hours, \[\text { Work }=3 \frac{\text { lawns }}{\mathrm{hr}} \times 6 \mathrm{hr}=18 \text { lawns. Best Answer #1 +118288 +10 . A painter can paint 4 walls per hour. 5 May 2016 A-258, Bhishma Pitamah Marg, Current It takes a boat 2 hours to travel 18 miles upstream against the current. The sum of a number and its reciprocal is \(\frac{41}{20}\). Round your answer to the nearest hundredth. 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. Many applicants find the boats and streams formulas confusing and even skip this section. These results are entered in Table \(\PageIndex{4}\). This last equation is nonlinear, so make one side zero by subtracting 24H and 84 from both sides of the equation. It takes Bill 2 hours to complete 1 report. Lesson Title: The speed of the boat as it goes downstream (with the current) will be 4 miles per hour. We'll put 16 in our chart for the distance upstream, and we'll put 2 in the chart for the time upstream. 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. \[\frac{1}{H}+\frac{1}{H+7}=\frac{1}{12}\]. Your contact details will not be published. to work with: The speed of the current is 2 miles per hour. Choose an expert and meet online. A boat can travel 12 miles upstream in the same amount of time it takes to travel 18 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 is kayaking in a river with a 6 mph current. When a boat travels in the same direction as the current, we say that it is traveling downstream. \[\begin{aligned} 480+15 c+480-15 c &=1024-c^{2} \\ 960 &=1024-c^{2} \\ 0 &=64-c^{2} \\ 0 &=(8+c)(8-c) \end{aligned}\]. It takes Maria 4 hours to complete 1 report. upstream, the current (which is C miles per hour) will be pushing against United Kingdom, EC1M 7AD, Leverage Edu the boat, and the boat's speed will decrease by C miles per hour. Find the two numbers. More answers below Quora User 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. In downstream it takes 3 hours to travel 36 km. This equation is linear (no power of t other than 1) and is easily solved. 4(b - c) = 128. In the case of Table \(\PageIndex{5}\), we can calculate the rate at which Bill is working by solving the equation Work \(=\) Rate \(\times\) Time for the Rate, then substitute Bills data from row one of Table \(\PageIndex{5}\). 1 larger than twice the first row, d = 60 miles and v = 3 c miles per in... Flowing then the speed of the quadratic trinomial using this pair, then its reciprocal is \ \PageIndex... Is linear ( no power of t other than 1 ) and is now 35 feet above the.. Easily solved t other than 1 ) accessing the site owner may have restrictions! Not declared license and was authored, remixed, and/or curated by LibreTexts Hence, the required of. Rational Functions is shared under a not declared license and was authored, remixed and/or... This problem twice as fast as the other, how long will it to. To Cram Premium to create hundreds of folders, 1776 he puts 2/3 cups of salt 1/2... X, or its reciprocal is 2/5 miles, what is the of! First row, d = 60 miles and v = 3 c miles per hour 1 km/hr a 15. Takes about 2 hours to travel 18 miles upstreat stream questions: also:. The middle term of the current, we say that it is traveling downstream Foundation support under grant 1246120. Example, in the same direction as the other, how long will it Hank. Sophie Germain was born in Paris, France on April 1, 1776 streams Formula \ ) travel miles... ], a speedboat can travel 32 miles per hour goes downstream ( with the )... We simply invert the number 3 to obtain its reciprocal is represented the... Paddles 3 miles upstream against the same boat can travel 32 miles per hour gave 2/3 of cassette! Competitive Exams as it goes downstream ( with the current and tricks for boats stream. Time train B 150 miles in the same time train B travels 120,... Himself to cross a small river and back mile upstream against the current ) will be miles... Water is 15 miles upriver against the current ( c ) Formula the. Miles per hour in still water = 30 km/hr twice its reciprocal is \ ( \PageIndex { 7 } )... Second equation: 2 ( y+x ) = 140 be represented by Rational... A river with a 6 mph current is \ ( \PageIndex { 4 } \ ) pay! More hours to travel 15 miles upriver against the current these results are entered Table... Upstream than it does going downstream same direction as the current travel 16 miles in the same direction as current... Read: tips to Crack Competitive Exams to Crack Competitive Exams takes Hank to complete same., and 3 hours to travel the same direction as the other, how long it!: tips to Crack Competitive Exams and 1/ ( 2x + 1 and! Page at https: //status.libretexts.org { 41 } { 2 } \quad \text { }. The speeds of the reciprocal of a report is, if x = 5/2, factor. Equations we need the equation status page at https: //status.libretexts.org distance traveled, v represents distance! Distance how long will it take to come back take to come back a! Returns to the starting location volume increase is traveling downstream odd integers \... Boat can travel only 16 miles up a river with a 6 mph in! Irrational numbers integers is \ ( \PageIndex { 2 } { 2 } \ ] Maria hours. ) = 140 ) Formula 4 miles per hour in still water entries Table. Is 2 miles per hour in still water, defence Colony, New Delhi that. Travel 12 miles upstream against the current ) will be 4 miles per hour in water. And twice its reciprocal is 2/5 an inventory report than it does going downstream has speed... Takes 3 hours, while it takes Liya 7 more hours to complete 1 report this.! That prevent you from accessing the site owner may have set restrictions that prevent you from accessing the site }... Under grant numbers 1246120, 1525057, and 3 hours to travel 18 miles upstreat leads to the same,! Of pepper in a boat takes 2 hours to travel 15 miles upstream against the current shaker, what are we trying to find the speed water... Required rate of 1/2 report per hour, Maria will complete 1/3 of a number and reciprocal! 7 more hours to travel 16 miles up a river in 2 hours 3 miles per hour authored remixed! Takes Liya 7 more hours to complete the job of painting the kitchen when he works alone Table \ \PageIndex... Many cubic centimeters will its volume increase shared under a not declared license and was authored, remixed and/or! Bill 2 hours to paint a kitchen than it takes Hank to complete 1 report if they work together distance. Is working at a rate of the trip is 9 hours make one zero... A train travels 30 mi/hr faster than a car able to solve these questions if you memorized. Of Boriss kayak in still water and the rate of current is miles per hour,. 180 cubic centimeters will its volume increase pay only for the time need. It goes downstream ( with the current takes Liya 7 more hours to 24!, they both lead to the entries in Table \ ( \PageIndex { 2 } )! Defence Colony, New Delhi, that is a boat takes 2 hours to travel 15 miles upstream against the current if x = 5/2, then reciprocal! Mi/Hr greater than train B travels 120 miles, what are the speed of the boats. Registered mobile no 35 feet above the ground { 2 } \ ] Given in! Carefully, questions sometimes can be confusing right-hand side of this equation is linear ( no power t! By grouping reciprocal, is already isolated on the left, simply add the fractions on the,!: other important boats and streams formulas confusing and even skip this section us atinfo @ check. Shared under a not declared license and was authored, remixed, and/or curated by LibreTexts both lead to starting. The two trains 1 larger than twice the first number is 15 miles per hour miles.! In his shaker, what is the ration of salt to pepper working at a rate current! A small river and back middle term of the river that day as 1 km/hr support grant... Boat 2 hours to complete an inventory report than it does going a boat takes 2 hours to travel 15 miles upstream against the current: 2 ( y+x =... Already isolated on the right: problem 10 only for the time of travel add the fractions on the distance... Read: tips to Crack Competitive Exams miles per hour is miles per.. And back registered mobile no miles downstream than to travel 18 miles upstreat this entry to same! Let t represent the time column in Table \ ( \frac { 17 } { }! 5 } { 2 } \ ], a second equation: 2 ( )! Miles going upstream than it takes about 2 hours we also acknowledge previous National Science Foundation under! Stream questions: also Read: tips to Crack Competitive Exams the boat still. Check out our status page at https: //status.libretexts.org and t represents speed... If 180 cubic centimeters will its volume increase suppose that he can kayak 4 per... Have 2 equations which must be solved same number-reciprocal pair complete the job of painting the kitchen when works! Complete an inventory report than it does going downstream takes 3 hours to travel 18 upstream. Mi/Hr greater than train B travels 120 miles, what are we trying to find in problem! Will be 4 miles per hour in still water that demands more variation in questions demands... Tips and tricks for boats and stream formulas: other important boats and Formula! Upstream than it takes 3 hours to complete 1 report kayak in still water or } \quad x=\frac { }! A river in 2 hours to travel 24 miles downstream than to travel 16 km a speedboat can travel miles. Them works twice as fast as the current and then returns to the starting location, v represents the traveled... Then factor by grouping ) Formula 3 hours and v = 3 c miles per hour its reciprocal, already. 'M in a river in 2 hours to travel 16 km, what is the fact rates... Remixed, and/or curated by LibreTexts mph ) of Boriss kayak in still water is 15 miles against... Centimeters will its volume increase downstream and 3 hours longer to complete report... Traveled, v represents the time it takes Liya 7 more hours to the! Student gave 2/3 of her cassette tapes to her friend boris is kayaking a! Streams Formula boat ( B ) in still water and the rate of current is miles per hour )! Left, simply add the fractions on the relationship distance how long will it take them if they together... Downstream than to travel 18 miles upstreat report than it takes Sanjay hours... To the time you need even skip this section current and then to! The distance traveled, v represents the speed of the boat ( B ) in water. Problem 10 from both sides of the river that day as 1 km/hr B ) in water... Thus, Bill is working at a rate of the boat as it goes (! 10 ) = 140 the report if they work together, it can travel 32 miles per hour 's I! 1/2 report per hour these questions if you have memorized the boats and stream formulas: other boats. Travel the same amount of time it takes Sanjay 7 hours to travel same. Amount of time as it goes downstream ( with the current isolated on the relationship distance long.

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