Question

An airplane takes 8 hours to travel a distance of 5824 kilometers against the wind. The return trip takes 7 hours with the wind. What is the rate of the plane in still air and what is the rate of the wind?

Answer 1

Speed of plane in still air = 780 km/h

Speed of air = 52 km/hr

Explanation:

Let the speed of plane in still air = u km/h

Let the speed of air = v km/h

Against the air, the resultant speed = (u-v) km/hr

With the air, the resultant speed = (u+v) km/hr

Formula for speed is given as:

`Speed = (Distance)/(Time )`

Given that:

Distance = 5824 km

Time taken against the wind = 8 hours

Speed against the wind:

`u-v = (5824)/(8) \\\Rightarrow u-v = 728 ...... (1)`

Time taken with the wind = 7 hours

Speed with the wind:

`u+v = (5824)/(7) \\\Rightarrow u+v = 832 ...... (2)`

Adding (1) and (2):

`2u=1560\\\Rightarrow u = 780\ km/hr`

By equation (1):

`780-v=728\\\Rightarrow v = 52\ km/hr`

Speed of plane in still air = 780 km/h

Speed of air = 52 km/hr