Question

If a plane can travel 480 miles per hour with the wind and 440 miles per hour against the​ wind, find the speed of the wind and the speed of the plane in still air.

Part 1
What is the speed of the​ wind?
  

Answer 1

Let's assume the speed of the plane in still air is P and the speed of the wind is W.

When the plane is flying with the wind, its effective speed is increased by the speed of the wind. Therefore, the actual speed of the plane in this case is P + W. We are given that this speed is 480 miles per hour.

When the plane is flying against the wind, its effective speed is decreased by the speed of the wind. Therefore, the actual speed of the plane in this case is P - W. We are given that this speed is 440 miles per hour.

Using this information, we can set up two equations:

P + W = 480 (equation 1)
P - W = 440 (equation 2)

Adding equation 1 and equation 2 gives us:
2P = 920
P = 920/2
P = 460

Substituting P = 460 into equation 1 or equation 2 gives us the value of W:

460 + W = 480
W = 480 - 460
W = 20

Therefore, the speed of the wind is 20 miles per hour.