Hi, it will take as long as it takes ! Not very helpful I know. But make sure you give yourself enough time. Esp for med, as school deadlines are often quite some time before the UCAS deadline. But quite often teachers want to know you are making progress/ have first draft at the start of term.
The big issue for medicine though is that the PS isn't really a key part of the selection for interview process for most med schools. So barring red flags, they may look at it before or after interview. Or not at all. Many sift for interview based on a UCAT or GCSE or a mix of both.
The problem is that there are some that REALLY use it as a key part of their selection for interview process. Now if you have one of those then you can gear your apS to its requirements. If you have two or more it's more tricky to blend it. If you have 4 that don't care about it then ....
Your med schools are best decided strategically on the basis of your UCAT and GCSEs.
So if you haven't done your UCAT yet, or sense checked your strategic choices yet with the "which medical school megathread", and read your respective application policies in DETAIL then I wouldn't stress too much about it at this stage...
Good luck.