Well, I don't think it needs to be an analog clock, as long as it's
any clock that doesn't show AM and PM. Then, we just need
to find how long it takes the clock to gain 12 hours.
I see you're in Middle School, so you'll be flabbergasted and
delighted to find that this is a Least Common Multiple (LCM)
problem.
What we need to find is the LCM of (12 hours) and (63 minutes).
12 hours = (12 x 60) = 720 minutes,
so it's the LCM of 720 minutes and 63 minutes.
Prime factors of 63: 3, 3, 7
Prime factors of 720: 2, 2, 2, 2, 3, 3, 5
The LCM:
2 x 2 x 2 x 2 x 3 x 3 x 5 x 7 = 5,040 minutes
= 84 hours
= 7 x (12 hours)
= 3-1/2 days
6 AM Wednesday morning.
If the clock does show AM and PM, then before it can show
the correct time, it has to gain 24 hours, not just 12. That'll
take another 3-1/2 days, so it'll be back in sync after 7 days,
meaning 6 PM NEXT Saterday.
