That's not how it works. You aren't chasing the antelope at max speed, you're chasing the antelope at whatever speed is necessary to keep it from cooling down under a tree. If there are a few of you, you can spread out so that "tree" is towards danger at all times. The goal is not to beat the antelope in a race, the goal is to deny the antelope the ability to cool down, drink water and recharge its metabolism. If the animal is hanging out at the fringes of the plains, you chase it out into the middle where it can't recuperate and then you run it there until it can't run anymore. If there six of you sixty degrees apart, you can even run that thing in a circle. Things get even easier once you invent ranged weaponry. An animal will try a lot harder to get away from you if you can get within 10 feet than if you can get within 10 yards.