Solution to POTW #1: the broken pocketwatch

See this link for the original puzzle post.

Solution:

We know the watch was correct at 2:00am. Let’s make a table of times, showing both the actual time and the time that the watch shows:

Actual time	Watch time
2:00 am	2:00 AM
3:00 AM	3:36 AM
4:00 AM	5:12 AM
5:00 AM	6:48 AM
6:00 AM	8:24 AM

Voila! When the watch stopped, showing 8:24am, it was actually 6:00am. Since that was one hour ago, it must now be 7:00 am.

“Alternative” method: We can take an algebraic approach instead of making a table of values and hoping to get lucky. Let X denote the number of hours that have passed since 2:00 am, when the watch last showed the correct time. Then, we can set up an equation that represents the time that the watch shows:

The left-hand side says, “The watch shows 8:24am right now”. The right-hand side says, “It was 2, and every hour that passed, the watch gained 1 hour and 36 minutes.”

Solving for X yields X = 4. That is, 4 hours passed since 2:00am, so the actual time was 6:00am when the watch showed 8:24am. Again, since it’s now one hour later, the time must now be 7:00 am.