Question

Flying against the wind, an airplane travels 6300 kilometers in 7 hours. Flying with the wind, the same plane travels 3960 kilometers in 3 hours. What is the rate of the plane in still air and what is the rate of the wind?

Answer 1

Rate of Plane = 1110 km/hr

Rate of Wind = 210 km/hour

Explanation:

Let Vₐ = the velocity of the airplane

Let Vₓ = the velocity of the wind

When flying with the wind:

(Vₐ + Vₓ) x 3 hours = 3960

3Vₐ + 3Vₓ = 3960

3Vₓ = 3960 - 3Vₐ

Dividing the equation be 3 we get:

Vₓ = 1320 - Va

When flying against the wind:

(Vₐ - Vₓ) x 7 hours = 6300 km

7Vₐ - 7Vₓ = 6300

Substitute (1320 - Vₐ) for Vₓ and solve for Vₐ:

7Vₐ - 7(1320 - Vₐ) = 6300

7Vₐ - 9240 + 7Vₐ = 6300

14Vₐ = 15540

Va = 1110 km/hr

Rate of wind:

Vₓ = 1320 - Vₐ = 1320 - 1110

Vₓ = 210 km/hour