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.

What is the speed of the​ wind? blank mph

Let's assume that the speed of the plane in still air is x mph and the speed of the wind is y mph.

When the plane is flying with the wind, its effective speed is increased by the speed of the wind. Therefore, the speed of the plane with the wind is x + y mph.

When the plane is flying against the wind, its effective speed is decreased by the speed of the wind. Therefore, the speed of the plane against the wind is x - y mph.

Given that the plane can travel 500 miles per hour with the wind and 400 miles per hour against the wind, we can write the following equations:

x + y = 500 (equation 1)
x - y = 400 (equation 2)

Adding equation 1 and equation 2, we get:

2x = 900

Dividing both sides of the equation by 2, we find:

x = 450

Substituting the value of x into equation 1, we can solve for y:

450 + y = 500
y = 50

Therefore, the speed of the wind is 50 mph.

What is the speed of the plane in still​ air?

The speed of the plane in still air is 450 mph.