burning single CD with both Mac and PC software?????

[Shannon Nugent]

Hey guys I got a question,

here goes.
Is there a way that I can burn a single data CD over a period of time 
using both a Mac a a PC without having to reformat it every time I need 
to burn more data?  Im taking a class on Macromedia Director from 
Monroe County Community College.  We have the option of storing our 
files on a CD for backup.  That would be easier and less expensive for 
me as the only other backup I have is a 100MB zip drive.  I'm not sure 
how much file space I need,  but I know that media files,  such as we 
will be making,  can take up a lot of space after awhile.  I decided to 
use a CD-RW instead.  My problem is that I'm working with a Mac at home 
and of course they are on the PC side.  I have Macromedia Director MX 
at home,  so getting the work done is no problem.  But,  I need a way 
to burn the new data onto CD every time I backup files without having 
to reformat my CR-RW or something.  Either that or just have some way 
where I can sort of drag and drop files onto the CD,  both when I'm on 
the Mac (here) and on the PC (at school) without having any trouble on 
either side.  My job would be something like:

Do stuff on the mac
backup stuff on CD
transport to school
copy files to "H" drive on PC and work on them
Save files backup new work on CD (either writing over the old file or 
just adding a new file onto the CD)

Is there any way I can do that without having to reformat the disc 
every time (both on PC and the Mac),  or run into some kind of trouble?

And when I burn a CD on a mac the PC can read it,  right?