Question 1167546
It just "feels" like the airplane travels 225mi/hr and the wind is 25mi/hr.
----<br>

With the wind:  1000mi / 4hrs = 250mi/hr
Against the wind: 1000mi / 5hrs = 200mi/hr<br>

225mi/hr is right in the middle, and that is the airplane's speed in still air.
That leaves the wind at 25mi/hr to make up the difference.<br>

<pre>
Algebraic solution:
Let a = speed of airplane in still air
    w = wind speed
<br>
(1)   (a+w)*4 = 1000  -->  4a + 4w = 1000
(2)   (a-w)*5 = 1000  -->  5a - 5w = 1000

Multiply the first equation by 5/4:  
      (1')  5a + 5w = 1250
      (2)   5a - 5w = 1000

Add (1') and (2):   10a = 2250  --> a = 225   (airplane speed 225mi/hr)

    Plug this value into (1):  4(225) + 4w = 1000 -->  4w = 100 --> w = 25
            (wind speed is 25mi/hr)