A:
You can use one external hard drive to back-up multiple computers if you partition the hard drive. If you're using time machine, I assume you're backing up Macs. Here is a link to walk you through partitioning your hard drive: http://macs.about.com/od/applications/ss/diskutilitypart.htm
If this isn't the route you want to go, I'd recommend buying an external drive for each computer.