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 490 km downstream, then find the time taken by boat ‘B’ to travel 98 km upstream and 770 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 = 490/7 Or, 10x = 70 Or, x = 7 Therefore, upstream speed of boat ‘B’ = 9x – 2x = 7x = 49 km/hr Downstream speed of boat ‘B’ = 9x + 2x = 11x = 77 km/hr Required time taken = (98/49) + (770/77) = 2 + 10 = 12 hours
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