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

Hint

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

Answer

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

Solution

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References

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