A Question of Timing

"One day, on our way to the place of prayer, a slave girl ran into us. She was a psychic, and, with her fortunetelling, she made a lot of money for the people who owned her. She started following Paul around, calling everyone's attention to us by yelling out, "These men are working for the Most High God. They're laying out the road of salvation for you!" She did this for a number of days, until Paul, fed up with her, turned and commanded the spirit that possessed her, "Out! In the name of Jesus Christ, get out of her!" And it was gone, just like that." Acts 16:16-18 (The Message).

So, the question I have is: Why did Paul wait so long to cast the evil spirit out of her? Did he know from the first that is was demonic, or did it take a few days to figure it out? Could it be that she didn't want it cast out, or that nobody else did, so there was a lack of faith? Does anybody have any suggestions? The discussion is open.