And that's exactly the way early humans hunted. The method is called persistence hunting: https://en.wikipedia.org/wiki/Persistence_hunting
Humans run slowly, but human bodies can dissipate heat very efficiently through sweating, and this makes humans good long-distance runners. AFAIK, humans can outrun most other animal species.
So if I understand it correctly, the hunting method involves scaring your prey, running for a while(yay hyperactivity), using your big brain to figure out where the prey went and running again for a while. Rinse and repeat for many hours, until the prey literally dies from exhaustion.
I imagine persistence hunting as a series of puzzles while you literally can see your reward - no delayed gratification involved.