Question
The ratio of the speed of boats βAβ and βBβ in
still water is 8:9, respectively. The speed of the current is 25% of the speed of boat βAβ in still water. If boat βAβ takes 10 hours to travel 500 km downstream, then find the time taken by boat βBβ 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 βAβ and βBβ in still water be 8x km/hr and 9x km/hr Therefore, speed of the current = 0.25 Γ 8x = 2x km/hr According to the question, 8x + 2x = 500/10 Or, 10x = 50 Or, x = 5 Therefore, upstream speed of boat βBβ = 9x β 2x = 7x = 35 km/hr Downstream speed of boat βBβ = 9x + 2x = 11x = 55 km/hr Required time taken = (70/35) + (275/55) = 2 + 5 = 7 hours
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