Question 600011
Speed of the plane in calm air = 480 mph
Let speed of air = X mph

Effective speed of the plane with the wind = 480 + X
Effective speed of the plane against the wind = 480 - X

According to the question,
Time taken by the plane to travel 600 miles with the wind = Time taken by the plane to travel 480 miles against the wind

i.e. {{{600/(480+X)=480/(480-X)}}}  (using the formula Time = Distance/Speed)

i.e. {{{5/(480+X)=4/(480-X)}}}

i.e. 4*(480 + X) = 5*(480 - X)

i.e. 1920 + 4X = 2400 - 5X

i.e. 9X = 480

X = 480/9 = 53.33


So the speed of air is 53.33 mph