Scratched xbox 360 game? toothpaste method?

I just got the new borderlands 2 and I started playing it then I moved my Xbox from vertical to horizontal then it said cannot read disc so I checked and it had scratches on it I'm trying the baking soda toothpaste method as we speak and i think i can see the scratches going away but I'm not sure if it will really work how long does it actually take? Some people say 5 minutes and others say overnight