If a plane can travel 470 miles per hour with the wind and 430 miles per hour against the wind, find the speed of the wind and the speed of the plane in still air.
Let's call the speed of the plane in still air as "x" and the speed of the wind as "y".
When the plane is traveling with the wind, the effective speed is the sum of the speed of the plane in still air and the speed of the wind: x + y = 470
When the plane is traveling against the wind, the effective speed is the difference between the speed of the plane in still air and the speed of the wind: x - y = 430
Now we can solve these two equations simultaneously to find the values of x and y.
Adding the two equations together, we get:
(x + y) + (x - y) = 470 + 430
2x = 900
Dividing both sides by 2, we get:
x = 450
Substituting this value of x back into one of the original equations, we can solve for y:
450 + y = 470
y = 470 - 450
y = 20
Therefore, the speed of the plane in still air is 450 mph and the speed of the wind is 20 mph.