Find the speed of the wind.

Question

I beg of you to help me. A small Plane can travel 120 mph in still air. The plain can fly 700 miles with the wind in the same that it can travel 500 miles against the wind. Find the speed of the wind.

Answer 1

v = speed in still air = 120 mph

w = wind speed = ?

t = travel time in hours

(v + w)t = 700

(120 + w)t = 700 (equation 1)

(v - w)t = 500

(120 - w)t = 500 (equation 2)

From equation 1, get

t = 700/(120 + w)

From equation 2, get

t = 500/(120 - w)

It is the same t in both equations, so

700/(120 + w) = 500/(120 - w)

Solve for w.

(120 + w)/700 = (120 - w)/500

120 + w = 1.4(120 - w)

120 + w = 168 - 1.4w

2.4w = 48

w = 20 mph