A road cyclist travels 120 miles with the wind in 3 hours an

A road cyclist travels 120 miles with the wind in 3 hours and 120 miles against the wind in 5 hours. Find the speed of the wind.

Solution

Assume the speed of the wind to be x miles/hr and the speed of the cyclist
to be y.
With the wind, the combined speed is x+y, x + y = 120/3 = 40 ...(1)
Against the wind, the (reduced)speed is x-y, x - y = 120/5 = 24 ...(2)
By (1)-(2),we have 2y = 16, so y = 8 miles/hr
Answer: the speed of the wind is 8 miles per hr