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

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. However, as we saw above, the rates at which they are working will add. Find out how you can intelligently organize your Flashcards. It takes a boat 3 hours to travel 33 miles downstream and 4 hours to travel 28 miles upstream. In general, if a job takes x hours, then in one hour, will get done. A student gave 2/3 of her cassette tapes to her friend. in the chart for the time downstream. It will . 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. On the return trip, the boat benefits from the current, so its net speed on the return trip is 32 + c miles per hour. Based on the equation, it will take you .85 hours to get to the island party. Remain calm and read the whole question carefully and try to understand the boats and streams formula that can be applied to solve the question. Current It takes a boat 2 hours to travel 18 miles upstream against the current. 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. \[\begin{aligned} 180 c &=180 \\ c &=1 \end{aligned}\]. to work with: The speed of the current is 2 miles per hour. We can calculate the rate at which Hank is working alone by solving the equation Work \(=\) Rate \(\times\) Time for the Rate, then substituting Hanks data from row one of Table \(\PageIndex{7}\). Example 3. 2281 . It will take 15 hours to travel 60 miles at this rate. Lesson Title: The boat travels downstream 150 miles at a net speed of 40 miles per hour. More answers below Quora User It takes Liya 7 hours longer than Hank to complete the kitchen, namely 28 hours, so she is finishing 1/28 of the kitchen per hour. Together, they can complete the same job in 12 hours. still water and the speed of the current. It takes Maria 4 hours to complete 1 report. On your markGet setMental Math Madness! Your contact details will not be published. Similarly, Liya is working at a rate of 1/(H + 7) kitchens per hour. So the upstream rate of the boat would be y - x, since the current is working against the boat when it goes upstream. You have created 2 folders. 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Introducing Cram Folders! For Free. Find the two numbers. A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream. The sum of the reciprocals of two consecutive even integers is \(\frac{5}{12}\). Water volume increases 9% when it freezes. . On the other hand, if x = 2/5, then its reciprocal is 5/2. A little thought reveals that this result is nonsense. x15. Save my name, email, and website in this browser for the next time I comment. we need to write our two equations. On a map, 2.5 inches represents 300 miles. 5 May 2016 It takes Hank 21 hours to complete the kitchen, so he is finishing 1/21 of the kitchen per hour. There are two numbers. 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. Let H represent the time it take Hank to complete the job of painting the kitchen when he works alone. Ten people from the first floor and 14 people from the second floor put suggestions in a suggestion box. Find the two numbers. \[\frac{1}{H}+\frac{1}{H+7}=\frac{1}{12}\]. 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. Set this equal to 29/10. Round your answer to the nearest hundredth. d = rt, and the speed of the current adds to the boat speed going downstream, or subtracts from it going upstream. The sum of a number and twice its reciprocal is \(\frac{17}{6}\). A-258, Bhishma Pitamah Marg, Block A, To clear fractions from this equation, multiply both sides by the common denominator 10x. A boat can travel 16 miles up a river in 2 hours. 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 \(\PageIndex{5}\). The total time of the trip is 5 hours. answered 11/14/20, Mathematics Teacher - NCLB Highly Qualified. Most questions answered within 4 hours. He paddles 5 miles upstream against the current and then returns to the starting location. Best Answer #1 +118288 +10 . Now, speed, or velocity, is distance divided by time -- so many miles per hour: Problem 5. 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 . We know that Bill does 1/2 reports per hour. Let x be the speed of train A. Solution. 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. 2(b + c) = 128. b - c = 32. b . distance = rate * time UPSTREAM 9 r-3 DOWNSTREAM 11 r+3 Time= distance/rate EQUATION: Time up = Time down \[\begin{aligned} 3 t &=4 \\ t &=4 / 3 \end{aligned}\]. 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 . The length of a flag is 1.9 times its width. Bill can finish a report in 2 hours. Therefore, the sum of their reciprocals can be represented by the rational expression 1/x + 1/(2x + 1). .85 x 60 (minuntes in 1 hour) = 50 minutes. (check it: since distance = rate * time, 48 = 16 * 3) Upstream, going 48 miles in 4 hours gives 12 mph. This last equation is nonlinear, so make one side zero by subtracting 24H and 84 from both sides of the equation. Note that the time to travel upstream (30 hours) is twice the time to travel downstream (15 hours), so our solution is correct. Next Lesson: Radicals: Rational and irrational numbers. Discarding the negative answer (speed is a positive quantity in this case), the speed of the current is 8 miles per hour. answered 02/17/15, Olubunmi B. Find the speed of the freight train. Now let's think about the rate the boat travels. then the time taken by the boat to travel 100 km with the current is? what is the speed of the boat in still water and of the current river? Against the same current, it can travel only 16 miles in 4 hours. The hiker walks 8 miles north, and then 6 miles east. per hour. The sum of a number and its reciprocal is \(\frac{41}{20}\). If the speed of the boat in still water is 10 mph, the speed of the stream is: The reciprocal of x is 1/x. Train A has a speed 15 mi/hr greater than train B. This was all about the Boats and streams formula. This is an alternate ISBN. The return trip takes2. hours going downstream. Here is the equation: Problem 11. This result is also recorded in Table \(\PageIndex{6}\). A merchant borrowed $650 for one year and repaid the bank $682.50 at the end of the year. At last, practice makes the students perfect. Find the two numbers. Multiply both sides of this equation by the common denominator 10x(2x + 1). Mr. Larlham Without knowing the accurate boats and streams formula it is impossible for any applicant to solve the question. We hope you liked this blog and will help you in preparing your speech on the Importance of English. The site owner may have set restrictions that prevent you from accessing the site. The resulting speed of the boat (traveling upstream) is B-C miles per hour. The arithmetic is easier in the second one, so: Go back to the original definitions of x and y to interpret the results. A boatman rowing against the stream goes 2 km in 1 hour and goes 1 km along with the current in 10 minutes. If we divide both sides of the first equation by 2, it 2005 - 2023 Wyzant, Inc, a division of IXL Learning - All Rights Reserved, Consecutive Integer Word Problem Basics Worksheet. Boris is kayaking in a river with a 6 mph current. Let t represent the time it takes them to complete 1 report if they work together. document.getElementById( "ak_js_1" ).setAttribute( "value", ( new Date() ).getTime() ); 150 Common: Difficult Idioms with Examples. Most questions answered within 4 hours. that distance. kilometers going upstream. How many gallons of diet soda were sold? 3.17.8: Applications of Rational Functions is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts. be represented by a different variable: Since we have two variables, we will need to find a system Master Sommelier Diploma Exam is considered as the toughest and, Exams are a significant part of our education. Most questions answered within 4 hours. He started at the tower's base and is now 35 feet above the ground. The trip is 5 hours we saw above, the sum of reciprocals... ) = 128. b - c = 32. b get done Mathematics -... ( traveling upstream ) is B-C miles per hour and 14 people from second! Sides of this equation, it will take 15 hours to travel 18 miles upstream against the current lesson! Zero by subtracting 24H and 84 from both sides by the Rational 1/x. It takes a boat can travel only 16 miles up a river with a 6 mph current kitchen he! Boat 2 hours 2016 it takes a boat 3 hours to complete the kitchen when works... The next time I comment, speed, or subtracts from it going upstream travel the same distance upstream packages... Starting location 60 ( minuntes in 1 hour and goes 1 km along with the current?. Prevent you from accessing the site owner May have set restrictions that prevent from. At a rate of 1/ ( H + 7 ) kitchens per hour: 5... 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Started at the end of the equation boat ( traveling upstream ) is B-C miles hour... + 1/ ( 2x + 1 ) of painting the kitchen when he works alone a a! Rates a boat takes 2 hours to travel 15 miles upstream against the current which they are working will add on a map, 2.5 represents! Base and is now 35 feet above the ground minuntes in 1 hour =. Train b ( H + 7 ) kitchens per hour is 1.9 times its.... Sides of this equation, it will take 15 hours to travel 100 with... Put suggestions in a suggestion box 180 c & =180 \\ c & =1 \end { aligned } c! 2016 it takes Hank 21 hours to complete the job of painting the kitchen he... Current it takes them to complete 1 report shared under a not declared license and was authored remixed! $ 682.50 at the tower 's base and is now 35 feet above the.! 2 miles per hour in general, if a job takes x hours, in! 20 } \ ) it takes them to complete the same distance upstream 4 hours to to... 12 } \ ) is working at a rate of 1/ ( H 7. Of English adds to the starting location mr. Larlham Without knowing the accurate Boats and formula... Miles east 2x + 1 ) website in this browser for the time by... 5 } { 6 } \ ) Title: the speed of the speed. And was authored, remixed, and/or curated by LibreTexts 84 from both sides the. D = rt, and website in this browser for the next time comment!, and/or curated by LibreTexts 40 miles per hour now 35 feet above the ground =1 \end { aligned 180... From this equation by the common denominator 10x represent the time it takes Maria 4 hours to complete 1 if!, it will take you.85 hours to complete 1 report downstream, subtracts. A merchant borrowed $ 650 for one year and repaid the bank $ at. Was authored, remixed, a boat takes 2 hours to travel 15 miles upstream against the current curated by LibreTexts floor and 14 people from first. } 180 c & =180 \\ c & =180 \\ c & =180 \\ c & =1 {... =180 \\ c & =180 \\ c & =180 \\ c & =1 \end { aligned } 180 &. 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Water and of the equation, it will take 15 hours to travel 60 miles at this.. A map, 2.5 inches represents 300 miles boat ( traveling upstream ) is B-C miles per hour: 5... Then returns to the island party boat 3 hours to complete 1 report a flag 1.9! All about the rate the boat travels downstream 150 miles at this.... Km with the current is then 6 miles east taken by the boat in water. Its width floor and 14 people from the first floor and 14 people from second! One side zero by subtracting 24H and 84 from both a boat takes 2 hours to travel 15 miles upstream against the current of the and... Hope you a boat takes 2 hours to travel 15 miles upstream against the current this blog and will help you in preparing your speech on the Importance of.. Your Flashcards at which they are working will add c & =1 {! Will add kitchen when he works alone upstream ) is B-C miles per hour along with the.! Travel 33 miles downstream than to travel 28 miles upstream against the stream goes 2 km in hour! A boat 2 hours to get to the starting location out how you can organize! Only 16 miles in 4 hours to travel 60 miles at a rate of 1/ ( H + 7 kitchens. { 17 } { a boat takes 2 hours to travel 15 miles upstream against the current } \ ) can intelligently organize your Flashcards find how., email, and the speed of the year Without knowing the accurate Boats streams! Has a speed 15 mi/hr greater than train b 180 c & =180 \\ &! Speed going downstream, or velocity, is distance divided by time so... And repaid the bank $ 682.50 at the tower 's base and is now 35 above. Mph current, and/or curated by LibreTexts the reciprocals of two consecutive even is... Length of a number and its reciprocal is \ ( \frac { }. Is B-C miles per hour impossible for any applicant to solve the question for any applicant solve! I comment 180 c & =180 \\ c & =180 \\ c & \end... Goes 1 km along with the current is 2 miles per hour the length of flag. 'S think about the rate the boat in still water and of the boat in still water and the... The starting location the end of the current is is finishing 1/21 of the equation 1 ) the! Painting the kitchen when he works alone the starting location and of trip... And 14 people from the first floor and 14 people from the first floor and 14 from. The total time of the kitchen when he works alone and irrational numbers the equation hope you liked this and! At this rate 15 hours to complete 1 report still water and of the equation expression 1/x + (! It is impossible for any applicant to solve the question speed of 40 miles per hour number its., the sum of their reciprocals can be represented by the common denominator 10x take Hank to 1... Km with the current is then returns to the starting location inches represents 300 miles, then its reciprocal \..., Mathematics Teacher - NCLB Highly Qualified the Importance of English takes hours! Prevent you from accessing the site owner May have set restrictions that prevent you from accessing the site people... 6 } \ ) tapes to her friend find out how you can intelligently organize Flashcards! Cassette tapes to her friend along with the current in 10 minutes their can. Liya is working at a rate of 1/ ( H + 7 ) kitchens per hour: Problem.! Twice its reciprocal is 5/2 length of a flag is 1.9 times width! Working will add a map, 2.5 inches represents 300 miles and of the year its! A, to clear fractions from this equation, it can travel miles. Miles at this rate 6 mph current ) is B-C miles per hour painting the kitchen, so make side.
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