'Running' in the Bible

The letters were sent in the name of King Ahasuerus and stamped with his ring, and they were taken by men on horseback, going on the quick-running horses used for the king's business, the offspring of his best horses:

So the men went out on the quick-running horses used on the king's business, wasting no time and forced on by the king's order; and the order was given out in Shushan, the king's town.