If a plane can travel 500 miles per hour with the wind and 400 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 P mph and the speed of the wind is W mph.
When the plane is flying with the wind, its effective speed is P + W mph.
When the plane is flying against the wind, its effective speed is P - W mph.
According to the given information:
P + W = 500 ----(Equation 1)
P - W = 400 ----(Equation 2)
Adding Equation 1 and Equation 2, we have:
2P = 900
P = 450
Substituting the value of P in Equation 1:
450 + W = 500
W = 500 - 450
W = 50
Therefore, the speed of the plane in still air is 450 mph and the speed of the wind is 50 mph.