Final answer:
The wind speed is calculated by setting up an equation using the effective speeds of the plane flying with and against the wind over equal times. After solving, we find that the wind speed is approximately 28.57 mi/h. However, this answer does not match any of the given options, suggesting a potential error in the question or options.
Step-by-step explanation:
The question asks us to determine the rate of the wind when a plane with a speed of 400 mi/h can fly 75 miles with the wind and 65 miles against the wind in the same amount of time. Let's denote the wind speed as 'w'. When the plane flies with the wind, its effective speed is (400 + w) mi/h. Against the wind, the plane's effective speed is (400 - w) mi/h. Using the formula distance = speed × time, and knowing that the time is the same for both distances, we can set up the following equation:
(400 + w) × t = 75
(400 - w) × t = 65
Dividing the first equation by the second gives us:
(400 + w) / (400 - w) = 75 / 65
Now we solve for 'w':
(400 + w) / (400 - w) = 15 / 13
13(400 + w) = 15(400 - w)
5200 + 13w = 6000 - 15w
28w = 800
w = 800 / 28
w = 28.57 mi/h
Since the wind speed must be one of the given options, we know it must be approximated to the nearest option. Therefore, the rate of the wind is approximately 30 mi/h, but this is not one of the available options, indicating a possible error in the initial question or the set options. We need to reevaluate the calculations or the question to ensure accuracy. As a tutor, I would advise checking the question and the answer choices given for any possible mistakes.