Problema Solution
An airplane took 4 hours to fly 3600 miles against headwind. The return trip took 3 hours with the headwind. Find the speed of the plane in still air and the speed of the wind.
Answer provided by our tutors
p = airplane speed (mph)
w = wind speed (mph)
(3600 miles)/(p - w) = 4
(3600 miles)/(p + w) = 3
=> 3600 = 4(p - w)
3600 = 4p - 4w
900 = p - w
=> p = 900 + w
=> 3600/(p + w) = 3
3600/((900 + w) + w) = 3
3600/(900 + 2w) = 3
3600 = 2700 + 6w
900 = 6w
w = 150
=> 3600/(p - 150) = 4
3600 = 4p - 600
4200 = 4p
p = 1050
The airplane's speed is 1050 mph and the windspeed is 150 mph.