Two friends, Joe and Moe, were born in May, one in 1932, the other a year later. Each had an antique grandfather clock of which he was extremely proud. Both of the clocks worked fairly well considering their age, but one clock gained ten seconds per hour while the other one lost ten seconds per hour.

On a day in January, the two friends set both clocks correctly at 12:00 noon.
"Do you realize," asked Joe, "that the next time both of our clocks will show exactly the same time will be on your 47th birthday?"
Moe agreed.

Who is older, Joe or Moe?

Since one clock gains as much time every hour as the other loses, the next time both clocks will show exactly the same time is when one has gained 6 hours and the other has lost 6 hours, since antique grandfather clocks have a 12-hour cycle.

If one clock gains 10 seconds per hour, it will gain one minute in 6 hours, one hour in 6*60=360 hours, and 6 hours in 6*360=2160 hours, or 90 days.

Now, the clocks are synchronized in January, and will agree again in May, and the intervening time is 90 days. The only way this can be true is if this occurs in a non-leap year and the clocks are synchronized on January 31, since 28 days in February + 31 days in March + 30 days in April = 89 days, leaving May 1st as the 90th day.

Joe tells us the clocks will align again on Moe's 47th B-day. If Moe was born in 1933, he would turn 47 in 1980, which is a leapyear, which does not work for this scenario. Therefore Moe was born in 1932 and Joe was born in '33, making Moe older.

Posted by Bryan on 2003-08-01 10:24:26