Flying against the wind, an airplane travels 5400km in 9 hours. Flying with the wind, the same plane travels 2700km in 3 hours. What is the rate of the plane in still air and what is the rate of the wind?

Question

Flying against the wind, an airplane travels 5400km  in 9 hours. Flying with the wind, the same plane travels 2700km in 3 hours. What is the rate of the plane in still air and what is the rate of the wind?

anonymous · Answer

You have two equations: Let AP = air plane km/h; Let W= wind km/h

Against the wind: 5400km/9h = AP - W

With the wind: 2700km/3 = AP + W

Rearrange the second equation: 900km/h - AP = W

Substitute into the first equation: 600km/h = AP - (900km/h - AP) which reduces to
1500 = 2AP So AP = 750km/h

Substitute AP into the second equation: 900km/h - 750km/h = W

So W = 150km/h