It will come as a surprise that a fit human can outrun almost any animal, including the horse, over a long enough distance.
I reproduce this quote from this the article "The Human Body is Built for Distance".
Most mammals can sprint faster than humans - having four legs gives them the advantage. But when it comes to long distances, humans can outrun almost any animal. Because we cool by sweating rather than panting, we can stay cool at speeds and distances that would overheat other animals. On a hot day, the two scientists wrote, a human could even outrun a horse in a 26.2-mile marathon.
The distance from Mount Carmel to Jezreel is about 50 km (see Wikipedia: Tel Jezreel)
Over this distance, a fit Elijah could easily our run, or at least stay ahead of the chariot pulled by horse(s). Thus, the factoid contained in 1 Kings 18:46 is quite credible, especially if the "hand of the Lord" strengthened him.
And the hand of the LORD came upon Elijah, and he tucked his cloak into his belt and ran ahead of Ahab all the way to Jezreel.
No teleportation required.
There is some indirect Bible evidence for this. In 2 Sam 18, news of the battlefront was dispatched, not by available horse & rider, but by a very fit (human) runner (V25, 26). This was also the case in 2 Chron 30:6, 10, Amos 2:14, 15, Est 3:13, 15, etc.