Why run something down when you can lie in wait for it? It would seem that for survival, the ability to run faster than the thing that's chasing you to eat you would be more critical than running down prey.
Why expend that kind of energy for that long when there are far easier things to find and eat that don't require that kind of energy output. I cannot imagine that some pre-human is going to chase things for those kind of long distances anyway. They'd be getting too far from home.
So what would the evolutionary advantage be to be able to outrun ANY creature for those kind of long distances?
Why don't you go ask all of the creatures that chase down their prey and also are slower than some other predator?