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