If a plane can travel 490 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.
What is the speed of the wind? mph
Let's call the speed of the plane in still air "p" and the speed of the wind "w".
When the plane is flying with the wind, its effective speed is the sum of the speed of the plane and the speed of the wind: p + w = 490 mph.
When the plane is flying against the wind, its effective speed is the difference between the speed of the plane and the speed of the wind: p - w = 410 mph.
We now have a system of two equations with two unknowns:
p + w = 490 ...(1)
p - w = 410 ...(2)
Let's add equations (1) and (2) to eliminate the variable "w":
(p + w) + (p - w) = 490 + 410
2p = 900
p = 450 mph
Now, substitute the value of "p" into equation (1) to solve for "w":
450 + w = 490
w = 490 - 450
w = 40 mph
Therefore, the speed of the wind is 40 mph.