When we walk next to a walking horse, it is not that hard to keep up. However, changing the pase, we easily lose distance. Walking through the park a human has a walking speed from 4 to 5 km/h. But we can speed things up and go to over 12km/h, Olympic sprinter Usain Bolt even runs with a speed of 35 km/h! Of course this all has to do with the context we run in as well. The speed of 35 km/h is possible for a short distance, but don't ask Usain to keep that speed for over an hour or less...
Time to compare. A walking horse has a speed of about 4 to 7 km/h, there is a wide range as we can decide to keep the horse in a collected walk or a free walk or extended walk or ... However when the horse is changing to a trot it easily speeds up to 12km/h, but completely untamed is when the horse is changing to canter. Our four-legged friend will then easily run at a speed of 20km/h to even 50 or 60 km/h. And this is just the speed of warmblood horses, we are not even referring to the racehorses who can speed up a bit more!
So think twice before you decide to take your horse for a 'running competition'...