Suppose you go 75 mph for 53 miles, 55 mph for 21 miles and 35 mph for 3 miles... what is your average speed?

You might want to get a second opinion, but this is how I figure it:
Multiply each speed by the distance
75mph X 53m
55mph X 21m
35mph X 3m
Then add each of the products together = 5235
Then divide that by the number of miles traveled = 77
5235/77=67.987
Average speed = 68mph

I would compute the time for each speed, then add up total time used.
Then, divide total distance by total time. All based on: Distance equals Rate times Time.

Multiply each speed by the distance
75mph X 53m
55mph X 21m
35mph X 3m
Then add each of the products together = 5235
Then divide that by the number of miles traveled = 77
5235/77=67.987
Average speed = 68mph

HOPE THAT HELPS YOU!