If it's only 13 miles then maybe it's not a fast ride, but tires make a LOT of difference (instant 2-4 mph depending on how much the change is).
Whether or not you change the tires, could be it's going to be one of those "who IS that chick on the mountain bike who's kicking butt?" scenarios
Important consideration: if you're on the wrong equipment, you're a lot less likely to like it.