It is an online homework question that I am stumped on! All I know is that I travel to work at 80mph and from I travel 20mph, and it wants my average speed or avgV!

It's going to be (80+20)/2.

To make you understand it better is 80 mph over some distance D (call it trip #1) and 20 mph over a distance on ( trip 2)

Thus you traveled 2 times over the same distance. Hence the 2.

Agreed that 50 is the arithmetic mean of the two velocities. But if the question is looking for the average speed over the round trip, in the sense of \frac{\text{total distance covered}}{\text{total time}} , then you'd want to factor in that you spent 4 times as long traveling at 20 mph.

Suppose the one-way commute was 80 miles. Then it takes 1 hour to get to work, and 4 hours to get home (why the rush to get to the office, yet so reluctant to return home? :)).

Then you've traveled 160 miles in 5 hours, for an average of...

Actually... If it's a round trip, then your average velocity would be 0. Velocity is your displacement/time. If you're arriving back at the same point, then your displacement from the final position to the starting position is 0/time. So 0 units/time units.