Question
The ratio of the speed of boats ‘A’ and ‘B’ in
still water is 8:9, respectively. The speed of the current is 25% of the speed of boat ‘A’ in still water. If boat ‘A’ takes 10 hours to travel 500 km downstream, then find the time taken by boat ‘B’ to travel 70 km upstream and 275 km downstream. (Note: Both the boats are rowing in the same stream.)Solution
Let the speeds of boats ‘A’ and ‘B’ in still water be 8x km/hr and 9x km/hr Therefore, speed of the current = 0.25 × 8x = 2x km/hr According to the question, 8x + 2x = 500/10 Or, 10x = 50 Or, x = 5 Therefore, upstream speed of boat ‘B’ = 9x – 2x = 7x = 35 km/hr Downstream speed of boat ‘B’ = 9x + 2x = 11x = 55 km/hr Required time taken = (70/35) + (275/55) = 2 + 5 = 7 hours
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