Small Off Grid Sound System 12V

[Ravioli]

I want to upgrade my jbl Partybox 300, which is a battery powered boombox by adding an aditional subwoofer. Would it be possible to hook up a Sub and Amp directly to a car battery? I was thinking of purchasing second hand one, something like the Edge EDB10A-E2, it has a built in amp, which is the reason I'm considering it. Another option would be the AXTON AXB25P Sub. I know theses aren't amazing subs, but they would be fine for what I need them for.
Do you guys think this would be a doable setup? How big would the battery have to be to power only the subwoofer? Was thinking of a 40 ah car battery.

Thanks