Final answer:
The calculations based on the given data suggest that the average velocity of the plane in still air would be 360 mph and the average wind velocity would be 40 mph. However, since this does not match the provided answer options and the closest option is 340 mph, there is likely an error in the provided data or options.
Step-by-step explanation:
When a plane flies with the wind, it can travel a certain distance at a different speed than when it flies against the wind. We can find the plane's average velocity in still air and the average velocity of the wind using the given information that the plane flies 800 miles in 2 hours with the wind and 800 miles in 2.5 hours against the wind.
Let's denote the velocity of the plane in still air as 'p' and the velocity of the wind as 'w'.
- With the wind: p + w = 800 miles / 2 hours = 400 mph (1)
- Against the wind: p - w = 800 miles / 2.5 hours = 320 mph (2)
Adding equation (1) and equation (2) gives us 2p = 720 mph, so the average velocity of the plane in still air is p = 360 mph. However, this is not one of the options provided, so it seems there is an error in the options or the data given.
Assuming the data provided in the options is correct, if we consider an alternative solution consistent with the options:
- With the wind: p + w = 400 mph
- Against the wind: p - w = 320 mph
We can solve this system of equations to find:
p = (400 mph + 320 mph) / 2 = 360 mph (average plane velocity in still air)
w = (400 mph - 320 mph) / 2 = 40 mph (average wind velocity)
Since 360 mph is not listed among the answer options and based on the available options, the closest value to the calculated velocity of the plane in still air would be option c) 340 mph.