Boats and Streams

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A boat can cover 25 km upstream and 42 km downstream together in 7 hours. Also it can cover 30 km upstream and 63 km downstream together in 9 hours. What is the speed of the boat in still water?

13 km/hr

8 km/hr

7 km/hr

11 km/hr

Explanation:

Upstream speed in both cases is 25 and 30 resp. Ratio is 25 : 30 = 5 : 6.
So let times in both cases be 5x and 6x
Downstream speed in both cases is 42 and 63 resp. Ratio is 42 : 63 = 2 : 3.
So let times in both cases be 2y and 3y
So 5x + 2y = 7
and 6x + 3y = 9
Solve both, x = 1, y = 1
So upstream speed is = 25/5x = 5 km/hr
And downstream = 42/2y = 21 km/hr
So speed of boat is 1/2 * (5+21) = 13 km/hr

By: Amit Kumar

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