If a plane can travel 480 miles per hour with the wind and 420 miles per hour against the wind, find the speed of the wind and the speed of the plane in still air?
Let's assume the speed of the plane in still air is represented by "x" miles per hour, and the speed of the wind is represented by "y" miles per hour.
When the plane is flying with the wind, it can travel at 480 miles per hour, so the equation is:
x + y = 480
When the plane is flying against the wind, it can travel at 420 miles per hour, so the equation is:
x - y = 420
To find the speed of the wind and the speed of the plane in still air, we need to solve these two equations as a system of linear equations.
First, let's add the two equations together to eliminate "y":
(x + y) + (x - y) = 480 + 420
2x = 900
x = 450
Now, we can substitute the value of x into any of the original equations to find the value of y. Let's use the first equation:
450 + y = 480
y = 480 - 450
y = 30
Therefore, the speed of the plane in still air is 450 miles per hour, and the speed of the wind is 30 miles per hour.