How long does it take to reinstall my iMac operating system

Depends on lots of factors, may be only a half hour as John Galt says, or 48 hrs like my slow internet connection on 2011 iMac took.

Perhaps a half hour or so.

My personal best was about ten days (DSL)

You win LOL, wasn't going to mention that it crashed the first 2 times at 99% & 40+hours each time. :)