Flying against the wind, an airplane travels 3850 km in 7 hours. Flying with the wind, the same plane travels 4350 km in 5 hours. What is the rate of the plane in still air and what is the rate of the wind?

The rate of the plane in still air is 710 km/hr and the rate of the wind is 160 km/hr

Explanation:

Let Va = the velocity of the airplane

Let Vw = the velocity of the wind

When flying with the wind:

(Va+Vw) * (5 hours) = 4350

5Va + 5Vw = 4350

5Vw = 4350 - 5Va

Vw = 870 - Va

When flying against the wind:

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

7Va - 7Vw = 4200

Substitute 870-Va for Vw and solve for Va:

7Va - 7 (870-Va) = 3850

7Va - 6090 + 7Va = 3850

14Va = 9940

Va = 710 km/hr

Rate of wind:

Vw = 870 - Va

= 870 - 710

= 160 km/hour

Therefore, the rate of the plane in still air is 710 km/hr and the rate of the wind is 160 km/hr