Question

Flying against the wind, an airplane travels 4500km in 6 hours. Flying with the wind, the same plane travels 2910 kilometers in 3 hours. What is the rate of the plane in still air and what is the rate of the wind?

Answer 1

Let a denote the airplane's speed in still air, and w the windspeed.

When the plane flies against the wind, it can travel an average speed of

(4500 km) / (6 h) = 750 km/h

so that

a - w = 750 km/h

Flying with the wind, it moves at a speed of

(2910 km) / (3 h) = 970 km/h

so that

a + w = 970 km/h

Add the two equations to eliminate w and solve for a :

(a - w) + (a + w) = 750 km/h + 970 km/h

2a = 1720 km/h

a = 860 km/h

Subtract them to eliminate a and solve for w :

(a - w) - (a + w) = 750 km/h - 970 km/h

-2w = -220 km/h

w = 110 km/h