Question

If a plane can travel 480 miles per hour with the wind and 380 miles per hour against the​ wind, find the speed of the wind and the speed of the plane in still air.

Answer 1

Let's call the speed of the plane in still air "p" and the speed of the wind "w".

When the plane is traveling with the wind, its speed is p + w. We are told that this speed is 480 miles per hour.
So, p + w = 480.

When the plane is traveling against the wind, its speed is p - w. We are told that this speed is 380 miles per hour.
So, p - w = 380.

Now we have a system of two equations with two unknowns:

p + w = 480 (equation 1)
p - w = 380 (equation 2)

To solve this system, we can add the two equations together:

(p + w) + (p - w) = 480 + 380
2p = 860
p = 430

Now, substitute the value of p back into one of the equations to find the value of w. Let's use equation 1:

430 + w = 480
w = 480 - 430
w = 50

Therefore, the speed of the plane in still air is 430 miles per hour, and the speed of the wind is 50 miles per hour.