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Dec 15, 2014 at 15:45 comment added Tonny I'm much more familiar with humans speeds than with horses. I would say normal human walking speed with a 20 kg backpack on decent terrain is 5-6 km/h (3-3.75 miles) and can be maintained for 8-9 hours a day. Modern day military forced marches do about 8-9 km/h (5-6 miles), but is usually limited to 3-4 hours duration. Roman legionnaires where expected to be able to do a daily 30 km (22 miles) march under 5 hours with approx. 25 kg of load. No human will do 7.5 miles per hour with just walking. With light load American Indian runners could do that all day alternating between run and walk.
Dec 15, 2014 at 14:26 history edited glenatron CC BY-SA 3.0
Added more of a description of a day's travel.
Dec 15, 2014 at 14:10 comment added glenatron Depends on your human walking-speed, but if that's coming to around 7.5 miles per hour, that probably would be viable. There isn't a great difference between travel on roads or cross country except that well maintained roads won't mean having to skirt around obstacles. I agree on the handwaving- an affinity-bound horse would make life a lot easier, especially if the rider is aware of their discomfort.
Dec 15, 2014 at 12:52 comment added Tonny I think I already covered most of the basic concerns you raise regarding dealing with horses over prolonged travel in my original question and with the various comments on the answers. (A number of those can be "hand-waived" due to the magic bond between rider and horse. The horse wouldn't wander of during the night. Rider is aware of the horses well-being at all times. And supplemental feed in small portions I already calculated in.) Your speed estimate seems OK for cross-country. For roads/trails an average of twice human walking speed for 10 hours a day seems doable.
Dec 15, 2014 at 11:05 history answered glenatron CC BY-SA 3.0