One solution would be to leave the 40 foot rope in the canyon. Not ideal, but could be a safer option than dropping a weighted pack onto yourself. Fix the 40 ft to the anchor, tie a rap ring to the end and rappel down. Rig the 120 ft off of the rap ring and transfer onto it (same technique as passing a knot in a single rope). Pull the 120', then when you get out of the canyon make your friend who mis-informed you about the beta go run the canyon again and retrieve the rope you left there. Thanks for providing some midnight entertainment for my insomnia, Tom.