On your way to class one morning, you leave home and walk at 3 m/s east towards campus. After exactly one minute you realize that you've left your physics assignment at home, so you turn around and run, at 6 m/s, back to get it. You're running twice as fast as you walked, so it takes half as long (30 seconds) to get home again.

Note that you covered 180 m before turning around.

Analyzing the 90 second out-and-back trip, what is your average speed?

1. zero
2. 4 m/s
3. 4.5 m/s
4. 5 m/s
5. 9 m/s

Average speed is the total distance covered divided by the total time.
That works out to 360 m / 90 s = 4 m/s

What is your average velocity?

1. zero
2. 1.5 m/s West
3. 3 m/s West
4. 4 m/s West
5. none of the above

Average velocity is the net displacement divided by the total time.
Since the net displacement is zero, v_avg = 0.