Two Clocks
Mad Ade has two clocks in his living room. Once they're synchronized, the correct time shown on the clocks is noon. One clock keeps time accurately; the other gains time such that after only 45 minutes it shows that an hour has passed. When can Mad Ade expect the two clocks to again both read 12 o'clock, and will the correct time be noon or midnight?
Answer
The two clocks would both read 12 o'clock in 36 hours and the correct time would be midnight.
When the fast clock reaches 12 o'clock midnight the first time,
the other clock (the correct one) will be showing 9pm.
Since it takes the fast clock just 3/4 of an hour to show a move of an hour on its face,
it will take 12 x 3/4 hours, which is 9 hours, to show the time as 12 midnight.
In 9 more hours the fast clock will read 12 noon, while the accurate clock will read 6am.
In 9 more hours, the fast clock will read 12 noon, and the accurate clock will read 12 midnight,
solving Mad Ade's problem.
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