I think you add the extra til if you could add "in order" in front of the "to" in the English sentence without changing the meaning. For example, this sentence could be rephrased as "The girl needs time in order to learn."
As a native English speaker I can verify jacquijohnson's comment about "in order to...". This is just another way of saying "for the purpose of..."; but more often than not, people will just say "to...", depending on the context. In the given sentence it would be acceptable.
So i'm a native dane, and you wouldn't say "Pigen behøver tid til at studere", but you'd actually say "Pigen har brug for tid til at studere"