An aircraft flew 2 hours with the wind. The return trip took 3 hours against the wind. If the speed of the plane in still air is 180 miles per hour more than the speed of the wind, find the wind speed and the speed of the plane in still air.
+128460 Let the wind speed = S
Let the rate of the plane in still air = 180 + S
So with the wind the plane's rate = (180 + S + S) = (180 + 2S)
Against the wind the plane's rate = (180 + S - S) = (180)
And Time * Rate = Distance....so......equating distances we have that
2 (180 + 2S) = 3 (180) simplify
360 + 4S = 540 subtract 360 from both sides
4S = 180 divide both sides by 4
S = 45 (mph) = wind speed
180 + S = 180 + 45 = 225 (mph) = plane's rate in still air
