Question

If a plane can travel 40 miles per hour with the wind and 390 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?
  
mph

Answer 1

Let the speed of the plane in still air be represented by x miles per hour.
The speed of the wind can be represented by y miles per hour.

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

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

Given that the plane can travel 40 miles per hour with the wind (x + y) and 390 miles per hour against the wind (x - y), we can set up the following equations:

x + y = 40 (equation 1)
x - y = 390 (equation 2)

Add equation 1 and equation 2:

(x + y) + (x - y) = 40 + 390
2x = 430

Divide both sides of the equation by 2:

2x/2 = 430/2
x = 215

Substitute the value of x into equation 1 to find the value of y:

215 + y = 40
y = 40 - 215
y = -175

However, the speed of the wind cannot be negative, so we discard this solution.

Therefore, there is no wind speed that satisfies both conditions of the plane's speed.