Take into account:
x = speed of the airplane
y = speed of the air
consider that the product in between time and speed is equal to the distance traveled in the time.
Then, if the airplane took 3 hours complete 600 miles, agaist the wind, you have that the distance traveled by the airplane is 3x without wind. The speed of the wind decelerates the airplane. The "distance traveled by the wind is 3y"
Then, when you subtract the previous terms you obtain:
3x - 3y = 600 factorize 3 left side
3(x - y) = 600