How far can a man on horseback travel in one day?

Oh how I love this question! First, how many horses?
On one horse at a forced pace would be about 50 miles. A man in good condition can handle the same distance on foot. If you don't care if the horse survives you can double that. One horse, one rider and you might do 200 miles in 24 hours. The horse might be dead when you hit the finish line, but the rider would survive.
Lots of other things should be thrown into the equation. Terrain and the
geography and the riders knowledge of both. Weather, temperature and
available water would be important factors to consider. The physical
condition and training of both the horse and rider should be evaluated.
I've stayed in the saddle for a full day, but that was long, long ago. My
longest ride on a single horse was 336 miles in seven days. That was in
1950. I loved it then.