The short answer is, yes, under the Pathfinder rules, that's per round (about 6 seconds).
The longer answer is, it's complicated.
In combat, according to the rules, you can move your base speed per move action (allowing also for an attack in the same round). Or 4 times (3 times in heavy armor) your base speed for a full-round run action (but only in a straight line).
As the broom is "like the
http://www.d20pfsrd.com/magic/all-spell ... and-flight spell", which states "When using this spell for long-distance movement, you can hustle without taking nonlethal damage", that's basically 2 times the base speed per round.