An air plane can travel 560 miles per hour with the wind and 480

miles per hour against the wind. Determine the speed of the plane in
still air and the speed of the wind.

if the plane's speed is p, and the wind is w,

p+w = 560
p-w = 480

That should help.

To determine the speed of the plane in still air and the speed of the wind, we can use a system of equations. Let's denote the speed of the plane in still air as "p" and the speed of the wind as "w".

When the plane is flying with the wind, the effective speed of the plane is increased. Therefore, we can write the equation:

p + w = 560 ----(1)

When the plane is flying against the wind, the effective speed of the plane is decreased. Thus, we can write the equation:

p - w = 480 ----(2)

To solve this system of equations, we can use the method of elimination. By adding equations (1) and (2) together, we can eliminate the variable "w":

(p + w) + (p - w) = 560 + 480
2p = 1040
p = 520

Now, we substitute the value of "p" into one of the original equations to solve for the wind speed "w". Let's use equation (1):

520 + w = 560
w = 560 - 520
w = 40

Therefore, the speed of the plane in still air is 520 miles per hour, and the speed of the wind is 40 miles per hour.