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.