Final answer:
The calculated speed of the airplane in still air is 570 mph, which does not match any of the provided options (A-D). Therefore, this suggests there might be a mistake in the question, the units, or the options provided.
Step-by-step explanation:
The student is asking to find the speed of the airplane when given distances and wind speed for a trip with and against the wind. Let's let x represent the speed of the airplane in still air. When John flies with the wind, the airplane's effective speed is x + 75 mph, and against the wind, it is x - 75 mph.
The time it takes to fly a certain distance is equal to the distance divided by the speed. Since the times are equal, we can set up the equation:
3225 / (x + 75) = 2475 / (x - 75)
Cross-multiply to solve for x:
3225(x - 75) = 2475(x + 75)
Expanding both sides gives:
3225x - 241875 = 2475x + 185625
Now, subtract 2475x and add 241875 to both sides:
750x = 427500
Finally, divide by 750 to get the speed of the airplane:
x = 427500 / 750 = 570
So, the speed of the airplane in still air is 570 mph. However, this speed is not one of the options provided (A-D), meaning there might be a mistake in the question, the units given, or in the options provided. Therefore, none of the options A-D is correct based on the calculations.