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
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.