Help with a word problem

Question

A plane has a cruising speed of
150
miles per hour when there is no wind. At this speed, the plane flew
300
miles with the wind in the same amount of time it flew
200
miles against the wind. Find the speed of the wind.

Answer 1

Distance = Speed * Time

 

Let W = wind speed 

 

The speed of the plane with the wind is 150 + W

The speed of the plane against the wind is 150 - W. 

 

In the same time T, 

 

The plane flew 300 miles with the wind ==> 300 = (150+W) * T

The plane flew 200 miles against the wind ==> 200 = (150-W) * T 

 

Multiply these out to get

 

300 = 150*T + W*T

200 = 150*T - W*T 

 

Add these together to get 500 = 300*T, so T = (5/3) 

 

Plug this in to the first equation to get 

 

300 = (150 + W) * (5/3) 

180 = 150 + W

 

W = 30