Essentially, if the players decide to travel together (as a group) they have to travel at the speed of the slowest mount in the party, but I guess people on faster mounts can just do everything quicker, so don't incur the same penalties for their actions.
If faster riders decide to leave the slowest one behind, the slowest will be forced to deal with the law-men sooner. Racing horse riders could, in that situation, act like scouts, dashing ahead and back again without causing the law-men to progress any further on their account, but it will be the slow ones who are in the most danger here, which makes sense given the nature of this scenario!
It is, of course, a little abstract, but is really just a way to ensure the PCs on slow mounts feel the consequences!
I have tried using this method with my friend (who was riding a slow mule) and it, combined with the surprise hyena attack, has worked much better to create a sense of tension and peril for him. I think otherwise he would have sailed right through without incident, and the potential for exciting drama this adventure offers would have been missed.
The hyenas killed his mule in the ruins of Grift's Creek, just before he killed their matriarch, and he fled on foot. Thanks to the amount of failed GRIT checks the hyena attack caused, the law have arrived in Grift's Creek not long after he left, so the sense of imminent danger is very real now!