Cancel. A dog can run an average of 19 miles per hour, but the fastest dog breeds, such as a greyhound, can run up to 42 miles per hour at their top speed.Discover how fast dogs can run with information from a pet care specialist in this free video on dogs.ancel. A dog can run an average of 19 miles per hour, but the fastest dog breeds, such as a greyhound, can run up to 42 miles per hour at their top speed.