df output sorted by most recently modified?

[lhouk]

I run a shell script that captures the output from df and creates a text file that is fed to a tar command, the idea being that I want to back up all my filesystems. I was wondering if it would be possible to back up the most-recently-modified filesystem first, then the next-most-recently-modified filesystem, and so on. I checked the man page for df to see if it had an option to list the modification date for the filesystems so I could sort on the field, but no such luck. Any suggestions? (And thanks in advance to all who respond!)