HMMT 2006 A5

Tim has a working analog 12 -hour clock with two hands that run continuously (instead of, say, jumping on the minute). He also has a clock that runs really slow-at half the correct rate, to be exact. At noon one day, both clocks happen to show the exact time. At any given instant, the hands on each clock form an angle between $0^{\circ}$ and $180^{\circ}$ inclusive. At how many times during that day are the angles on the two clocks equal?