According to one Florida Campfire member an alligator can out run a quarter horse for several hundred yards over dry land. Evidently you aren't safe anywhere!
I think that's total BS. At least I know that African crocodiles can't.
I know for sure with the right head start I can out run one. Took my girlfriend "parking" one night, got out to take a leak, the tall grass between me and a little pond something started thrashing the grass. I ran wank in hand back to the safety of the car. And I'm here to tell about it.