We are also removing the rubber backing from a carpet we just pulled up. It's at least 15 years old. We've found either taking a putty knife and scraping (without the varnish, too much of a mess) or power sanding the rubber backing makes it come up quite easily. The power sander is quicker, but a lot noisier and a bit messier, while the putty knives take about 5 times as much time as the sander. Also rember to vacuum the dust left from the sander up often. It'll make your eyes red.