If you take one hour drive at an average speed of 65 mph, is it possible for another car with an average speed of 55 mph to pass you

Sure it is.  We only know the average speeds, but we don't know
how much of the time each car drove faster or slower. 

The averages only tell us who got to the end of their trip sooner. 
But there could have been a time ... or several times during the hour ...
when the 55mph car was blazing and passed the 65mph car.

In fact, the 55mph car could have been driving at 110 mph for the
first 29 minutes, then the last 1.83 miles at a speed of 3.5 mph.
His average would then be 55mph, even though he spent the first
29 minutes passing everybody and everything on the road in the
first 53.16 miles of his trip.