Question

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?

Answer 1

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