There are many animals that can run faster than humans.
There are not many that can run as far.

An incredible video of persistance hunting

"...we began adding meat to our diets around 2.6 million years ago, long before we developed advanced weapons like the bow and arrow, which was developed as recently as 50,000 years ago."

"We can run in conditions that no other animal can run in."

"Most animals would develop hyperthermia -- heat stroke in humans -- after about 10 to 15 kilometers" (6-10 miles)

- Harvard Anthropology Professor Daniel Lieberman, from physorg.com

So we began hunting by chasing our prey until it collapsed: Persistence Hunting.

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physorg.com article
Wikipedia
Google
U.S. State laws on atlatl (spear) hunting