Question

An airplane travels 720 in 3 hours with the wind. The return trip against the wind takes 4 hours. What is the wind speed and the speed of the airplane in still air?

Answer 1

Wind speed = 30 per hour, Airplane speed = 210 per hour.

Explanation:

Given:

An airplane travels 720 in 3 hours with the wind.

The return trip against the wind takes 4 hours.

Question asked:

What is the wind speed and the speed of the airplane in still air ?

Solution:

First of all we will find speed of airplane with the wind:-

`Speed=(Distance)/(Time)`

`=(720)/(3) \\ \\ =240`

Now, let speed of plane =
`p`

And let speed of wind =
`w`

Speed of of airplane with the wind will be:-

`p+w=240\ (equation\ 1)`

Similarly, we will find speed of airplane against the wind:-

`Speed=(Distance)/(Time)`

`=(720)/(4) \\ \\ =180`

Speed of airplane against the wind will be:-

`p-w=180\ (equation\ 2)`

Adding equation 1 and 2:-

`p+w+p-w=240+180\\ \\ 2p=420\\ \\ Dividing\ both\ sides \ by \ 2\\ \\ (2p)/(2) =(420)/(2) \\ \\ p=210`

Speed of plane =
`p` = 210 per hour.

Speed of wind =
`w` = ?

Taking from equation 1:-

`p+w=240\\ \\ 210+w=240\\ \\ w=240-210\\ \\ w=30\ per \ hour`

Speed of wind = 30 per hour.

Therefore, the wind speed is 30 per hour and speed of the airplane in still air is 210 per hour.