Question
A boat covers 45 km downstream in 90 minutes. If the ratio of the speed of the boat in still water to that of the speed of the stream is 5:3, respectively, then find the time taken by the boat to cover a distance of 15 km upstream.
Solution
ATQ, Speed of the boat downstream = (45/90)×60 = 30 km/h Let the speed of the boat in still water = 5x km/h Speed of stream = 3x km/h Speed of the boat downstream = 5x+3x = 8x km/h 30 = 8x x = 30/8 = 3.75 Speed of the boat in still water = 5×3.75 = 18.75 km/h Speed of the stream = 3×3.75 = 11.25 km/h Speed of the boat upstream = 18.75−11.25 = 7.5 km/h Time taken by the boat to cover the distance of 15 km upstream = (15/7.5) × 60 = 120 minutes
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