Mapping Center Answer:

First, you don't produce travel distances directly from a census tract shapefile.  You'd need a road network dataset (not just a shapefile, but something that contains weightings for speed limits, impedences for traffic lights, and stop signs, etc., and potentially additional time of day impedence weightings).  Most network analysis software has a drive time buffer function that will create or select the lines in the network dataset that are within a given drive-time of a point you enter.  You can then use that selection or set of lines to select census tracts--I would calculate a new field on the census tract to indicate that the tracts are within a drive-time of X for point Z.  That would allow you to code multiple drivetimes and locations into the same census tract dataset--making the demographic analysis (that I would expect somebody might do later) easier.