Alright, lets get started.
A light private plane can fly 120 mph in still air.
Suppose the speed of wind = x mph
Against the wind, speed of plane will be = 120-x
With the wind, speed of plane will be = 120+x
Flying against the wind, the plane can fly 320 miles, so time taken will be
t = ![\frac{320}{120-x}](https://tex.z-dn.net/?f=%5Cfrac%7B320%7D%7B120-x%7D)
With the wind, the plane can fly 640 miles, so time taken will be
![t = \frac{640}{120+x}](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7B640%7D%7B120%2Bx%7D)
Both times are given same, so
![\frac{320}{120-x}= \frac{640}{120+x}](https://tex.z-dn.net/?f=%5Cfrac%7B320%7D%7B120-x%7D%3D%20%5Cfrac%7B640%7D%7B120%2Bx%7D)
Cross multiplying
![320(120+x) = 640(120-x)](https://tex.z-dn.net/?f=320%28120%2Bx%29%20%3D%20640%28120-x%29)
Dividing from 320
![120+x = 2(120-x)](https://tex.z-dn.net/?f=120%2Bx%20%3D%202%28120-x%29)
![120+x = 240-2x](https://tex.z-dn.net/?f=120%2Bx%20%3D%20240-2x)
![3x = 120](https://tex.z-dn.net/?f=3x%20%3D%20120)
x = 40 mph
So, the speed of the wind is 40 mph. : Answer
Hope it will help :)