A friend's watch hands meet every 65 minutes — is it fast, slow, or accurate?
A friend pulls out his watch and says it isn't keeping perfect time: he's noticed that the minute hand and the hour hand are exactly together every 65 minutes. Does his watch gain or lose time, and by how much per hour?
Reveal the answer
It gains. On a perfectly accurate watch, the hands coincide every 65 5/11 minutes, not 65 — so if 65 true minutes pass between coincidences, the watch is running through its cycle faster than it should. Dudeney's answer: it gains 5/11 of a minute every 65 minutes, which works out to exactly 60/143 of a minute every hour.
— Henry Dudeney, Amusements in Mathematics — Thomas Nelson & Sons, 1917, Puzzle No. 59
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