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 hours to travel 700 km downstream, then find the time taken by boat ‘B’ to travel 140 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 = 700/7 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 = (140/70) + (220/110) = 2 + 2 = 4 hours
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