Does a Nikkor 55-300mm AF-s focus faster on a d7000 than a d3100?

I was just wondering since the d7000 has an internal focusing motor and the d3100 does not, though I'm pretty sure it doesn't matter.

No because it uses the motor in the lens. Lenses that use the body motor are quite slow to focus.
The d7000's more advanced AF system may cause any lens to start performing the focussing quicker but that's hard to distinguish.

Lol no… Get a 70-300mm