Respuesta :
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:-
[tex]Speed=\frac{Distance}{Time}[/tex]
[tex]=\frac{720}{3} \\ \\ =240[/tex]
Now, let speed of plane = [tex]p[/tex]
And let speed of wind = [tex]w[/tex]
Speed of of airplane with the wind will be:-
[tex]p+w=240\ (equation\ 1)[/tex]
Similarly, we will find speed of airplane against the wind:-
[tex]Speed=\frac{Distance}{Time}[/tex]
[tex]=\frac{720}{4} \\ \\ =180[/tex]
Speed of airplane against the wind will be:-
[tex]p-w=180\ (equation\ 2)[/tex]
Adding equation 1 and 2:-
[tex]p+w+p-w=240+180\\ \\ 2p=420\\ \\ Dividing\ both\ sides \ by \ 2\\ \\ \frac{2p}{2} =\frac{420}{2} \\ \\ p=210[/tex]
Speed of plane = [tex]p[/tex] = 210 per hour.
Speed of wind = [tex]w[/tex] = ?
Taking from equation 1:-
[tex]p+w=240\\ \\ 210+w=240\\ \\ w=240-210\\ \\ w=30\ per \ hour[/tex]
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.
