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 7.5 hours to travel 750 km downstream, then find the time taken by boat ‘B’ to travel 210 km upstream and 330 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 = 750/7.5 Or, 10x = 100 Or, x = 10 Therefore, upstream speed of boat ‘B’ = 9x – 2x = 7x = 70 km/hr Downstream speed of boat ‘B’ = 9x + 2x = 11x = 110 km/hr Required time taken = (210/70) + (330/110) = 3 + 3 = 6 hours
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