Six weeks gives you just enough time to get ready. Others have already said it-get the base miles increased and quickly . Do a long ride (at least 80 miles 2 weeks prior to the century). If the century has some climbing be sure and get in some 40-50-60 mile rides with some hills. The best way I've found to do the centuries is to simply pile on the miles and just get acclimated to riding 6-8 hours.
On ride day-you might think about breaking the ride down into three or four rides.....Just plan to get from point to point and don't think about what comes after until you get there. Once you get to 80-85 miles you'll be okay. The most challenging part might be the mind games so be prepared to be mentally tough.....
You can do it and will feel really, really rewarded afterwards. Worth all the training and challenge of the ride!! Just remember, as long as the bike is moving forward you're making progress and getting closer to the finish.