Question

Flying against the wind, an airplane travels 2610 kilometers in 3 hours. Flying with the wind, the same plane travels 8750 kilometers in 7 hours. What is the rate of the plane in still air and what is the rate of the wind?

Answer 1

200 km/hr

Explanation:

Let Va = the velocity of the airplane

Let Vw = the velocity of the wind

When flying with the wind:

(Va+Vw)*(4 hours) = 4000

4Va + 4Vw = 4000

4Vw = 4000 - 4Va

Vw = 1000 - Va

When flying against the wind:

(Va-Vw)*(7 hours) = 4200 km

7Va - 7Vw = 4200

Substitute 1000-Va for Vw and solve for Va:

7Va - 7(1000-Va) = 4200

7Va -7000 + 7Va = 4200

14Va = 11200

Va = 800 km/hr

Rate of wind:

Vw = 1000 - Va = 1000 - 800 = 200 km/hour