> Google says that horses can go up to 70 km/h (45mi/h).

That is the fastest speed for a Thoroughbred racehorse over a mile. It's not sustainable for long. The horse record for 100 miles is 17MPH, on a really good Arabian.[1] 6MPH is a good working pace for a horse. 8-12 MPH at the trot, which can be kept up for a hour or two by many horses in good condition.

[1] https://www.chronofhorse.com/article/world-endurance-record-...

There is a long distance man vs horse race, which is sometimes won by horse, and sometimes by man.