An airplane flew 4 hours with a 25 mph tail wind. The return trip against the same wind took 5 hours. How do you find the speed of the airplane in still air?
The speed of the plane is 225 mph.
To solve this task you can use the following system of equations:
Both equations come straight from the laws of cinematics (time equals distance divided by speed)
If you multiply both equations by the denominators you will get:
So you can write only one equation with the unknown
Answer: The speed of the plane without the wind is
First we calculate the distance:
Next we check the times:
a) with the wind
b) against the wind
Call the speed of the plane (in still air)
from the first equation:
substitute into the second: