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}](https://tex.z-dn.net/?f=Speed%3D%5Cfrac%7BDistance%7D%7BTime%7D)
![=\frac{720}{3} \\ \\ =240](https://tex.z-dn.net/?f=%3D%5Cfrac%7B720%7D%7B3%7D%20%5C%5C%20%5C%5C%20%3D240)
Now, let speed of plane = ![p](https://tex.z-dn.net/?f=p)
And let speed of wind = ![w](https://tex.z-dn.net/?f=w)
Speed of of airplane with the wind will be:-
![p+w=240\ (equation\ 1)](https://tex.z-dn.net/?f=p%2Bw%3D240%5C%20%28equation%5C%201%29)
Similarly, we will find speed of airplane against the wind:-
![Speed=\frac{Distance}{Time}](https://tex.z-dn.net/?f=Speed%3D%5Cfrac%7BDistance%7D%7BTime%7D)
![=\frac{720}{4} \\ \\ =180](https://tex.z-dn.net/?f=%3D%5Cfrac%7B720%7D%7B4%7D%20%5C%5C%20%5C%5C%20%3D180)
Speed of airplane against the wind will be:-
![p-w=180\ (equation\ 2)](https://tex.z-dn.net/?f=p-w%3D180%5C%20%28equation%5C%202%29)
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](https://tex.z-dn.net/?f=p%2Bw%2Bp-w%3D240%2B180%5C%5C%20%5C%5C%202p%3D420%5C%5C%20%5C%5C%20Dividing%5C%20both%5C%20sides%20%5C%20by%20%5C%202%5C%5C%20%5C%5C%20%5Cfrac%7B2p%7D%7B2%7D%20%3D%5Cfrac%7B420%7D%7B2%7D%20%5C%5C%20%5C%5C%20p%3D210)
Speed of plane =
= 210 per hour.
Speed of wind =
= ?
<u>Taking from equation 1:-</u>
![p+w=240\\ \\ 210+w=240\\ \\ w=240-210\\ \\ w=30\ per \ hour](https://tex.z-dn.net/?f=p%2Bw%3D240%5C%5C%20%5C%5C%20210%2Bw%3D240%5C%5C%20%5C%5C%20w%3D240-210%5C%5C%20%5C%5C%20w%3D30%5C%20per%20%5C%20hour)
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.