Wrong clocks

Saw this one on Professor Layton 2.

Puzzle

To analogue clocks hang side by side on a wall. One of the clocks is slightly fast, the other slightly slow. One day at noon, you set both clocks correctly. After one hour you notice that the fast clock displays 1:01 and the slow clock reports the time as 12:59. Assuming the clocks continue to be fast and slow at the same rate, how long before both clocks agree on the time again?

Help

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Hint

When will the fast clock be one hour ahead? What will the slow clock display then?

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Answer

It will take 360 hours (15 days) for the clocks to display the same time as each other again.

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Solution

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References

Professor Layton and the Diabolical Box - sequel to the Curious Village. Another great Nintendo DS puzzle game.