Question

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. Determine the speed of the stream and that of the boat in still water.

Answer 1

Let the speed of the boat in still water be x km/h and speed of the stream be y km/h. Then the speed of the boat downstream = (x + y) km/h, and the speed of the boat upstream = (x – y) km/h

Also, time =distance/speed

In the first case, when the boat goes 30 km upstream, let the time taken, in an hour, be t₁. Then

t₁=30/x-y

Let t₂ be the time, in hours, taken by the boat to go 44 km downstream. Then t₂=44/x+y. The total time taken, t₁ + t₂, is 10 hours. Therefore, we get the equation

30/x-y  + 44/x+y =10   ......(1)

In the second case, in 13 hours it can go 40 km upstream and 55 km downstream. We get the equation

On substituting these values in Equations (1) and (2), we get the pair of linear equations:

Hence, the speed of the boat in still water is 8 km/h and the speed of the stream is 3 km/h.