Not sure where you got your number but they seem similar to the one I have in my old dnd 3.5 edition book.

a normal person would walk 36km per day, seems ok
But I think the horse is faster even for longer distances, but since I have never been on one, I only rely on dnd and common sense. There are different kind of horses too. Donkey ( not an horse but often used) is nearly as strong, much smaller and also slower, for example. I mean the Spanish used heavy cavalry against the Moor that used light cavalry, much faster. Useful for guerilla tactic or skirmishes, the where butchered on the field of battle against the tougher horses (more armored too). So some horse are good for speed wile other races are more strudy.

There are also other mean of transportation such as ships but when I look at the table here : (scroll down) SRD:Movement - D&D Wiki
I get confused because the distances in my book are in km and in miles on internet and nothing matches but it's the same version.
Ship with sails can usually move all day long so that is why they have greater distance and some are faster than walking too, but noit too much. If someone could walk all day long, he could do 70km or more maybe. That is as fast as some sail boat it seems.