Final answer:
The speed of the plane in still air is 564 mph and the speed of the wind is 187 mph.
Step-by-step explanation:
To find the speed of the plane in still air, we can use the concept of relative velocity. Let's assume that the speed of the plane in still air is x mph and the speed of the wind is y mph.
When the plane is flying with the wind, the effective speed of the plane will be x + y mph. We are given that the distance traveled is 938 miles and the time taken is 2 hours. Using the formula distance = speed * time, we can write the equation 938 = (x + y) * 2.
Similarly, when the plane is flying against the wind, the effective speed of the plane will be x - y mph. We are given that the distance traveled is 938 miles and the time taken is 3 hours. Using the same formula, we can write the equation 938 = (x - y) * 3.
Now, we have a system of equations that we can solve to find the values of x and y.
Solving these equations, we find x = 564 and y = 187. Therefore, the speed of the plane in still air is 564 mph and the speed of the wind is 187 mph.