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A person rows a distance of 20 km upstream and 15 km downstream in a total time of \(2 \frac{5}{12}\) hours. If the speed of the current is 4 km/h, then in how many hours can he row a distance of 64 km upstream?1. \(5 \frac{1}{3}\)2. \(4\frac{2}{3}\)3. \(5\frac{1}{2}\)4. \(4\frac{1}{4}\) |
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Answer» Correct Answer - Option 1 : \(5 \frac{1}{3}\) Given: A person rows a distance of 20 km upstream and 15 km downstream in a total time of 2(5/12) hours Speed of the current is 4 km/h Formula used: Distance = speed × time Speed in downstream = speed of the boat + speed of the stream Speed in upstream = speed of the boat - the speed of the stream Calculation: Let the speed of the boat be 'x' km/h Speed in downstream = x + 4 km/h Speed in upstream = x - 4 km/h Now , Time taken in downstream = 15/(x + 4) hours Time taken in upstream = 20/(x - 4) hours Total time = time of upstream + time of downstream ⇒ 2(5/12) = [15 /(x + 4)] + [20/(x - 4)] ⇒ x = 16 Now time taken to cover 64 km in upstream Time = 64/(x -4) ⇒ 64(/16 - 4) = 64/12 ⇒ 16/3 hours ∴ Boat will take 16/3 hours to complete 64 km in upstream. |
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