D&D 5E Fast travel and renting mounts doubts

[Herr der Qual]

Isn't that why people would travel with a spare horse? Switch out every 30 to 60 minutes so that one horse could rest while allowing you to travel faster than a person would walk for a day.

Ok, so I grew up on horses and we used to actually travel pretty long distances moving cattle by horse, I also once accepted a challenge to ride 100 km (62 miles) between two towns (we called it the Pony Express Charity Fundraiser) for a little background on my knowledge.

The accepted method of traveling quickly with a single horse is you give it an hour of walking at the start of the day, followed by trotting for 15 minutes (consider it a jog for a horse if you are unfamiliar about 10-12 mph) then you lope (just shy of a gallop, winds up being about 16 - 18 mph depending on how fast your horse runs) for 15 minutes, rinse and repeat, after about two hours of going between a trot and a lope you walk your horse for about half an hour, then you dismount for 15-20 minutes give yourself a break (trotting is very hard on your body, it takes a lot of effort because you need to move your body opposite to your horse's otherwise you get jarred every couple steps).

This puts the average single horse travelling speed for about 4 hours a day at 14 MPH on flat ground, sparse trees don't really slow you down, but deep sludgy ground make this impossible (swamps), you can lope through a forest but it's dangerous to you, the horse isn't going to hit anything but you can be taken off your mount by a thick low hanging branch pretty easily (I'd say for game purposes traveling above a trot in the forest requires a DC 18 concentration check to not be dismounted, and a 5% chance your horse breaks it's leg), horses excel at running uphill due to their heavily muscled hind quarters, you will actually find yourself trying to hold your horse back going uphill, but they balk at running downhill (if you force a horse to run downhill 35% chance of tripping, if it trips going down hill 20% chance of crippling itself).

At the end of a long day of travelling quickly on a single horse if the player doesn't let it walk around for at least an hour, the horse will be cramped the next day and not perform nearly as well. Hope this was helpful.