If a plane can travel 500 miles per hour with the wind 400 miles per hour against the wind, find the speed of the plane without a wind and the speed of the wind? What is the speed of the plane in still air?
450 mph
To find the speed of the plane without the wind and the speed of the wind, we can set up a system of equations based on the given information.
Let's say the speed of the plane without the wind is represented by "p" (in miles per hour) and the speed of the wind is represented by "w" (in miles per hour).
According to the given information, when the plane is flying with the wind, its effective speed is 500 miles per hour. This means that the actual speed of the plane (without the wind) is p, and the speed of the wind is w, so the effective speed is p + w.
Similarly, when the plane is flying against the wind, its effective speed is 400 miles per hour. This means that the actual speed of the plane (without the wind) is p, and the speed of the wind is w, so the effective speed is p - w.
Setting up these equations, we have:
p + w = 500 (equation 1)
p - w = 400 (equation 2)
Now, we need to solve this system of equations to find the values of p and w. We can do this by adding equation 1 and equation 2:
(p + w) + (p - w) = 500 + 400
2p = 900
p = 450
Now, we can substitute the value of p into either equation 1 or equation 2 to solve for w. Let's use equation 1:
450 + w = 500
w = 500 - 450
w = 50
Therefore, the speed of the plane without the wind (in still air) is 450 miles per hour, and the speed of the wind is 50 miles per hour.