Distances a horse can travel vary depending on the size and condition of the riders, mounts, weather, terrain, and condition of the roads. Medieval people traveled with everything they needed following in carts behind them. A train of this sort wouldn't move fast. Mounted knights-- all on well-conditioned destriers or palfreys -- would move fairly fast and cover upwards of 50 or 60 miles per day. However, traveling 20 to 30 miles a day would be considered a good day's journey.
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People in very good condition can sustain 30 miles per day on well-maintained, flat roads--although 20 miles is more reasonable/sustainable (Troops in WWII were expected to march 20 miles per day).
However,troops have been known to move 40 miles in a day, but they are so exhausted upon arriving they are nearly useless. General Patton marched his men about 25 miles per day during their famous march, maintaining this for 3-4 days.
Depends on the load size. Assuming it's a pioneer type wagon, 10-15 miles on average. In bad conditions, they might only make a mile. On the best of days, more like 20 miles.