Question
A boat can travel 8 km more in downstream than that in
upstream, in 4 hours while the difference between the time taken by the same boat to travel 120 km and 90 km, in still water, is 4 hours. Find the approximate time taken by the boat to travel 200 km in downstream and 120 km in upstream.Solution
Let the speed of boat in still water and speed of stream be 'x' km/hr and 'y' km/hr, respectively. According to question; (120/x) - (90/x) = 4 Or, (30/x) = 4 So, x = 7.5 Now, 4 x (7.5 + y) = 4 x (7.5 - y) + 8 Or, 30 + 4y = 30 - 4y + 8 Or, 8y = 8 So, y = 1 So, downstream speed of the boat = (7.5 + 1) = 8.5 km/hr And, upstream speed of the boat = (7.5 - 1) = 6.5 km/hr Required time taken = (200/8.5) + (120/6.5) ~ (24 + 19) ~ 43 hours
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