Flying with the wind, a small plane flew 360 miles in 2hours. Against the wind, the plane could fly only 300 miles in the same amount of time. Find the rate of the plane in calm air and the rate of the wind.

Question

Flying with the wind, a small plane flew 360 miles in 2hours. Against the wind, the plane could fly only 300 miles in the same amount of time. Find the rate of the plane in calm air and the rate of the wind.
I cant figure out how to solve this. Please help me

Jana · Answer

use the variables p for plane and w for wind and the equations:

(p+w)x 2hours = 360 miles
(p-w)x 2hours = 300 miles
divide by 2

p+w=180
p-w=150
combine the two equations so w cancels out

2p = 330
divide by 2 to get the speed of the plane.

p=165
put the plane back into the equation to get the rate of the wind

165+w = 180
w = 15m/h