If a plane can travel 450 miles per hour with the wind and 410 miles per hour against the wind, find the speed of the wind and the speed of the plane in still air.
Let's assume the speed of the plane in still air is represented by p, and the speed of the wind is represented by w.
When the plane is flying with the wind, the speed is increased by the speed of the wind. Therefore, the effective speed is p + w.
Similarly, when the plane is flying against the wind, the speed is decreased by the speed of the wind. Therefore, the effective speed is p - w.
Given that the plane can travel 450 miles per hour with the wind and 410 miles per hour against the wind, we have two equations:
p + w = 450 ...(1)
p - w = 410 ...(2)
We can solve these two equations to find the values of p and w.
Adding equation (1) and equation (2), we get:
2p = 860
p = 430
Substituting the value of p in equation (1), we get:
430 + w = 450
w = 450 - 430
w = 20
Therefore, the speed of the plane in still air is 430 miles per hour, and the speed of the wind is 20 miles per hour.