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

Answer:

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

Step-by-step 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:-

$Speed=\frac{Distance}{Time}$

         $=\frac{720}{3} \\ \\ =240$

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:-

$Speed=\frac{Distance}{Time}$

         $=\frac{720}{4} \\ \\ =180$

Speed of airplane against the wind will be:-

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

Adding equation 1 and 2:-

$p+w+p-w=240+180\\ \\ 2p=420\\ \\ Dividing\ both\ sides \ by \ 2\\ \\ \frac{2p}{2} =\frac{420}{2} \\ \\ p=210$

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.