50 miles per hour is the rate (speed) of the wind.
<u>Step-by-step explanation:</u>
Let consider the variable ‘x’ for speed of wind.
<u>Below we write two values of the speed of the airplane in the air in terms of ‘x’:
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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