Brake Controller Hookup 7 & 4 Way Installation Kit

I cannot find any information on how to hook this up to my vehicle. Here is a link to the item I am talking about.

http://etrailer.com/p.asp?etbc7

I has to main wires. One white and one black inside an insulated covering. A shorter purple and white wire and a 4 connector.

I have connect the 4 connector to my Suburban's existing 4 connector. I am unsure exactly how to connect the other wires.

My best guess is that the white short wire is a ground. The short purple goes to the brake controller.

What are the other long wires (long white and black) for and how should I connect them?

Thanks for any help.
Doug Bedient