1. The speed of a boat in still water is 8km/hr. It can go 15 km upstream and 22 km downstream in 5 hours. Find the speed of the stream.
1. The speed of a boat in still water is 8km/hr. It can go 15 km upstream and 22 km downstream in 5 hours. Find the speed of the stream.

Solution:

Let the speed of stream be x km/hr

Given, speed of boat in still water is 8km/hr.

So, speed of downstream = (8 + x) km/hr

And, speed of upstream = (8 - x) km/hr

Using, speed = distance/ time

Time taken by the boat to go 15 km upstream = 15/(8 - x)hr

And, time taken by the boat to return 22 km downstream = 22/(8 + x)hr

From the question, the boat returns to the same point in 5{{x}^{2}}-7x+296-320=0hr.

5{{x}^{2}}-7x+296-320=0

5{{x}^{2}}-7x-24=0

5{{x}^{2}}-15x+8x-24=0[by factorisation method]

5x(x - 3) + 8(x - 3) = 0

(x - 3)(5x + 8) = 0

x = 3

x = - 8/5

As the speed of the stream can never be negative, only the positive solution is considered.

Therefore, the speed of the stream is 3 km/hr.