How long does it take for Microsoft to repair an Xbox 360?

So my Xbox 360 keeps freezing when I'm playing zombies, and other games. I'm getting very annoyed and want to send my Xbox to get repaired since it is free, but I heard that it take like 3 months to fix and ship back. I have dropped my power brick about 15 feet straight down onto hardwood stairs because of a hole in the railing. Could that be causing the freezing or is it the Xbox itself? How long would it take to repair and ship back? Btw, I am shipping from Pennsylvania.