From the basic equation: distance = rate * time
From Miami to London (against the wind): distance = (500 - wind speed) * 8
From London to Miami (with the wind): distance = (500 + wind speed) * 7
Equating both gives:
(500 - wind speed) * 8 = (500 + wind speed) * 7
wind speed = 33.33 mph
The average speed of the wind is 33.33 mph.