I'll answer the question after the two trains leave the opposite stations traveling at different speeds and get to the level crossing. I mean, you did say "math", so I want to optimize the problem set.....
Anyway, so marathon is Jan 12, 2020 and would expect Jan 10, 2021....2020 is a leap year, so there is an extra day difference. I believe in regular years, a pass is good for 366 days--so a pass activated on Jan 1 would be good through Jan 1 the following year. But I don't know about leap years. If they DON'T give you the leap day, then this might affect when you might initialize your pass. If you did it on Jan 10, 2020 as you mention, which is a Friday, then it could expire Jan 9, 2021 (which would still be 366 days)--that would be a Saturday, and would not cover Sunday, Jan 10, 2021.
I am not a current AP holder, so "grain of salt". I'd call Disney and ask.