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?
Moe is born in 1932, and hence is older.
For the grandfather clocks to show the same time, the fast one must gain 6 hours, and the slow one lose 6 hours. This will take (6 hours)x(60 minutes/hour)x(60 seconds/minute) / (10 seconds/hour) hours, which is exactly 90 days.
If they set the clocks on January 31, 1979, they will agree again at noon on May 1, 1979 (each reading 6 o'clock). Hence this is Moe's 47th birthday.
If they had set the clocks in 1980 (had Moe been born in 1933), then the latest they could have agreed is April 30th, not may, due to 1980 being a leap year.
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