If a plane can travel 470 miles per hour with the wind and 390 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 assume the speed of the plane in still air is represented by "p" and the speed of the wind is represented by "w".
When the plane is traveling with the wind, the effective speed is the sum of the speed of the plane and the speed of the wind. Therefore, the speed with the wind is given by p + w = 470 mph.
Similarly, when the plane is traveling against the wind, the effective speed is the difference between the speed of the plane and the speed of the wind. Therefore, the speed against the wind is given by p - w = 390 mph.
We can now solve these two equations simultaneously to find the values of "p" and "w".
Adding the two equations: (p + w) + (p - w) = 470 + 390
gives us: 2p = 860
Dividing by 2, we find: p = 430 mph
Substituting this value back into one of the original equations: 430 + w = 470
we can find the value of "w" by subtracting 430 from both sides: w = 470 - 430
which gives us: w = 40 mph.
Therefore, the speed of the wind is 40 mph.