How long does it take for a potential employer to contact you after handing in a resume?

You don't wait. Part of what your future employer is looking for in a 16 year kid is responsibility and consistency. If you want the job you call back every day and ask for the manager, not the assistant manager, and don't settle for anyone else. When you do get him on the phone, ask him if he has made a decision yet, and that you are very interested in long term employment-- right through high school. Or go in and ask him in person. The people who "follow up" on their applications are the people who get the jobs. And don't be afraid that you are bugging him to death. He will remember you when it comes time to make the decision. He will remember that you were interested enough to check in with him every day. He will take your consistency and drive as a positive sign. You will get the job. If you want it bad enough.