an airplane travels at a rate of 250 miles/he with the wind and at a rate of 150 miles against the wind. what is the rate of the wind?

50 miles per hour is the rate (speed) of the wind.

Step-by-step explanation:

Let consider the variable 'x' for speed of wind.

Below we write two values of the speed of the airplane in the air in terms of 'x':

1. Subtract wind speed from airplane speed: 250 - x.

2. Add wind speed to the airplane speed against the wind: 150 + x.

And now, set these above two expressions equal to each other to find x (wind speed),

250 - x = 150 + x

2x = 100

x = 50 miles per hour