Nitpicking is my favorite drug.
It’s actually horses that cannot run continously. The famous Pony Express rode their horses in a “run a bit, walk a bit” fashion, which is the normal way to ride a horse long distance since antiquity.
The Pony Express was set up to provide a fresh horse every 10-15 miles and a fresh rider every 75-100 miles. 75 horses were needed total to make a one-way trip. Average speed was 10 miles per hour.
Horse speed at long distance with a rider on its back (not carrying weapons and armor) and changing to fresh horses along the way: (10mph x 1.6 = 16kmph) (16kmph / 3.6 = 4.4 meters per second
Marathon runners can run for hours at this sort of pace. They run the 42 km long race in about 2 hours. (42 km / 2 h = 21 kmph) (21 kmph / 3.6 = 5.83 meters per second).
Ultramarathon runners cover a distance of 100 km in about 6 hours. (100km / 6h = 16.67 kmph) (16.67 kmph / 3.6 = 4.63 meters per second). - Still faster than horses.
Thanks