Answer:
Rate of plane in still air = 1120 km/h
Rate of wind = 180 km/h
Step-by-step explanation:
Let the rate (speed) of the plane in still air = u km/h
Let the rate (speed) of the wind = v km/h
Formula for speed is:
![Speed = \dfrac{Distance}{Time}](https://tex.z-dn.net/?f=Speed%20%3D%20%5Cdfrac%7BDistance%7D%7BTime%7D)
Given that against the wind, airplane travels 7520 km in 8 hours.
The speed against the wind will be slower so,
Against the wind, speed = (u -v ) km/h
Using above formula:
![(u-v) = \dfrac{7520}{8} km/h\\(u-v) = 940 km/h ..... (1)](https://tex.z-dn.net/?f=%28u-v%29%20%3D%20%5Cdfrac%7B7520%7D%7B8%7D%20km%2Fh%5C%5C%28u-v%29%20%3D%20940%20km%2Fh%20.....%20%281%29)
Given that with the wind, airplane travels 6500 km in 5 hours.
The speed with the wind will be faster so,
With the wind, speed = (u +v ) km/h
Using above formula:
![(u+v) = \dfrac{6520}{5} km/h\\(u+v) = 1300 km/h ..... (2)](https://tex.z-dn.net/?f=%28u%2Bv%29%20%3D%20%5Cdfrac%7B6520%7D%7B5%7D%20km%2Fh%5C%5C%28u%2Bv%29%20%3D%201300%20km%2Fh%20.....%20%282%29)
Adding (1) and (2) to solve for u and v:
![2u = 2240\\\Rightarrow u = 1120\ km/h](https://tex.z-dn.net/?f=2u%20%3D%202240%5C%5C%5CRightarrow%20u%20%3D%201120%5C%20km%2Fh)
Putting u in (1):
![1120-u=940\\\Rightarrow u = 180\ km/h](https://tex.z-dn.net/?f=1120-u%3D940%5C%5C%5CRightarrow%20u%20%3D%20180%5C%20km%2Fh)
So, the answers are:
<em>Rate of plane in still air = 1120 km/h</em>
<em>Rate of wind = 180 km/h</em>
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