@ Lord Finnish, I copied down some information about that sort of thing a while ago from various websites, take a look:
Your figures look generally okay to me, but I think they exaggerate the speed of horseback travel a little - or at least, your numbers will apply to individual riders or small groups, but not to cavalry armies on the march.
Horses are much faster than humans over short distances, but they also get tired more quickly; so over long distances the humans will actually be faster. That doesn't apply if you are willing to ride your horse until it dies of exhaustion, but obviously that's not practical if you expect to need it later. It also doesn't apply if you have multiple horses and you switch to a different one whenever each gets tired. The Mongol hordes were famous for covering vast distances very quickly on horseback - but that's because each warrior had up to a dozen horses with him and could change regularly. Even then, a Mongol army performing a forced march would leave a broad trail of dead horses behind it.
For the record, the United States Army has formal regulations (published online) for how fast soldiers can march. Three miles per hour (5 kph) for 50 minutes, then a ten minute break; a longer break at lunchtime; walking for eight hours. That way, soldiers can cover exactly 20 miles (32 km) in a day. A trained, healthy solder can repeat that for multiple days while carrying full equipment. A forced march officially means marching for longer each day rather than faster: if you walk for 10 hours instead of 8 you'll cover 25 miles per day, but will be exhausted at the end of it.
As far as I know, Roman legions marched at pretty much the same pace. Such things don't really change.
Another factor to bear in mind is the availability of food and provisions. If you have depots - or inns - pre-positioned along the route to supply the marching troops and horses, they can keep going all day. Similarly if you have supply carts, or even better a fleet carrying provisions sailing parallel to the route of the marching soldiers. But if you have to keep on stopping to forage for food - or worse, to graze your horses - you aren't going to be travelling nearly as far that day.
Likewise if you have to look for a campsite instead of being able to check into a hostel every night - and especially if, like the Romans, you want to fortify your campsite against attack instead of just letting each group of soldiers pitch their tents wherever they like. Arranging that takes time.
In short, if you're an army on the march into unknown territory - even if it's friendly or allied - your speed is going to be probably less than half the speeds listed in that chart.
