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 8.5 hours to travel 680 km downstream, then find the time taken by boat ‘B’ to travel 84 km upstream and 220 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 = 680/8.5 Or, 10x = 80 Or, x = 8 Therefore, upstream speed of boat ‘B’ = 9x – 2x = 7x = 56 km/hr Downstream speed of boat ‘B’ = 9x + 2x = 11x = 88 km/hr Required time taken = (84/56) + (220/88) = 1.5 + 2.5 = 4 hours
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