What do you mean by long distance? 30 or 40 miles? I seriously doubt that any land bound creature alive can outrun a human at distances of 50 miles or more. The human body is built for fabulous endurance. The Tarahumara indians were noted for their fantastic endurance and the ability to cover unbelievable distances in a days time.
The best of human endeavor in a 26 mile marathon is a little over 2 hours. An ostrich has been clocked at 45 mph over twenty minutes= 15 miles. It would take the human 1 hour at a world class marathon runner's pace to catch up to the ostrich if it stopped and stood still for an hour or so.
The odds of human success? About the same as the Dolphins chance of winning the Super Bowl.
About the pronghorn antelope: don't know the endurance, mileage wise. I'll try to find out.