Question 45

A boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours, it can go 40 km upstream and 55 km down-stream. The speed of the boat in still water is:

Solution

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Let us assume the upstream speed of the boat = u and the downstream speed = v

30/u+44/v=10

40/u+55/v=13

Consider 1/u=a, 1/v=b, these equations become

30a+44b=10

40a+55b=13

We get a=1/5 and b=1/11 Hence,  1/u=1/5 and 1/v =1/11 => u=5 and v=11

Assuming speed of boat in still water is x and the speed of stream=y

u=x-y=5

v=x+y=11

From these equations, we get x=8 km/hr

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