If a plane can travel 470 miles per hour with the wind and 410 miles per hour against the wind, find the speed of the wind and the speed of the plane in still air.

Question

If a plane can travel 470 miles per hour with the wind and 410 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 assume the speed of the plane in still air is denoted by p and the speed of the wind is denoted by w.

According to the given information, when the plane is flying with the wind, its speed is p + w (470 mph), and when it is flying against the wind, its speed is p - w (410 mph).

We can set up a system of two equations to represent this:
p + w = 470 ...(1)
p - w = 410 ...(2)

To solve this system, we can add equations (1) and (2) together:
(p + w) + (p - w) = 470 + 410
2p = 880
p = 440

Now, we can substitute the value of p back into equation (1) to find the value of w:
440 + w = 470
w = 470 - 440
w = 30

So, the speed of the plane in still air is 440 mph, and the speed of the wind is 30 mph.

If a plane can travel 470 miles per hour with the wind and 410 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 denoted by p and the speed of the wind is denoted by w.

If a plane can travel 470 miles per hour with the wind and 410 miles per hour against the wind, find the speed of the wind and the speed of the plane in still air.