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.
What has helped me determine if "til" is needed or not, is substituting the infinitive (to study) with the -ing form (studying). In this case: The girl needs time studying - does not make sense. Correct is: The girl needs time FOR studying. The "for" in the English sentence is an indicator that "til at" needs to be used in the Danish sentence, instead of only "at". This works in most cases, exceptions I have found so far are "have someone do something" or "get someone to do something" (have/få nogen til at gøre noget) which seem to be fixed constructs. I hope this helps someone :)