It was not said how the old man was travelling, and I doubt the horse was at a literal run. A carriage can go as fast as about 30 miles an hour on a modern road, but even in those conditions you should expect to break your carriage. On ancient roads, depending on condition, the speed limit for going “very fast” in a carriage could easily have been as low as about 10 miles per hour. If the old man was riding on an animal, or walking very fast, then he could have kept up for some time.
We at least know that the carriage wasn’t moving at its top speed because at the end of the story the horse sped up.
It was not said how the old man was travelling, and I doubt the horse was at a literal run. A carriage can go as fast as about 30 miles an hour on a modern road, but even in those conditions you should expect to break your carriage. On ancient roads, depending on condition, the speed limit for going “very fast” in a carriage could easily have been as low as about 10 miles per hour. If the old man was riding on an animal, or walking very fast, then he could have kept up for some time.
We at least know that the carriage wasn’t moving at its top speed because at the end of the story the horse sped up.