Plane took 1 hr LONGER to fly 480 AGAINST the wind than it t

Plane took 1 hr. LONGER to fly 480 AGAINST the wind than it took to fly the same distance WITH the wind. If wind speed is 20 mph, what is the speed of plane in calm air?

Solution

Let the speed of the plane in calm air be x mph
With the wind speed of the plane = (x+20)mph
Against the wind speed of the plane = (x-20) mph
Time taken to travel 480 miles with the wind = 480 / (x + 20) hrs
Time taken to travel 480 miles against the wind = 480 / (x - 20) hrs
Therefore according to the problem,
480/(x-20) - 480/ (x+20) = 1
==> 480x + 9600 -480x + 9600 = x^2 - 400
==> 19600 = x^2
==> x = 140
Therefore the speed of the plane = 140 mph