Evasion and Pursuit
In round-by-round movement, simply counting off squares, it’s impossible for a slow character to get away from a determined fast character without mitigating circumstances. Likewise, it’s no problem for a fast character to get away from a slower one.
When the speeds of the two concerned characters are equal, there’s a simple way to resolve a chase: If one creature is pursuing another, both are moving at the same speed, and the chase continues for at least a few rounds, have them make opposed Dexterity checks to see who is the faster over those rounds. If the creature being chased wins, it escapes. If the pursuer wins, it catches the fleeing creature.
Sometimes a chase occurs overland and could last all day, with the two sides only occasionally getting glimpses of each other at a distance. In the case of a long chase, an opposed Constitution check made by all parties determines which can keep pace the longest. If the creature being chased rolls the highest, it gets away. If not, the chaser runs down its prey, outlasting it with stamina.