In the most dangerous game Why does Rainsford swim toward pistol shots?

In Richard Connell's short story "The Most Dangerous Game", Rainsford does not swim towards pistol shots. Rather, after the second day of being hunted by General Zaroff, Rainsford hears what he thinks are his own shots echoing, leading him to realize that Zaroff had placed cartridges with blanks instead of bullets within his rifle