If a plane can travel 480 miles per hour with the wind and 380 miles per hour against the wind, find the speed of the wind and the speed of the plane in still air.
Let's call the speed of the plane in still air "p" and the speed of the wind "w".
When the plane is traveling with the wind, its speed is p + w. We are told that this speed is 480 miles per hour.
So, p + w = 480.
When the plane is traveling against the wind, its speed is p - w. We are told that this speed is 380 miles per hour.
So, p - w = 380.
Now we have a system of two equations with two unknowns:
p + w = 480 (equation 1)
p - w = 380 (equation 2)
To solve this system, we can add the two equations together:
(p + w) + (p - w) = 480 + 380
2p = 860
p = 430
Now, substitute the value of p back into one of the equations to find the value of w. Let's use equation 1:
430 + w = 480
w = 480 - 430
w = 50
Therefore, the speed of the plane in still air is 430 miles per hour, and the speed of the wind is 50 miles per hour.