College Math story problem

Question

A private airplane flew 420 miles in 3 hours with the wind. The return trip against the wind took 3.5 hours. Find the rate of the plane in calm air and the rate of the wind.

Answer 1

In this problem, the distances are equal.

Rate x time = distance

420 miles/ 3 hours = 140 mph with the wind

420 miles/3.5 hours = 120 mph against the wind

140 = x + wind

120 = x - wind

260 = 2x

x = 130

wind = 10

Check: (130 + 10)(3 hours) = 420 miles

and, (130 - 10)(3.5 hours) = 420 miles