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Let start from midnight 12 am or 0 hours. The two hands point in the same direction.

The minutes hand turns 360 degrees in one hour. So in one hour the minutes hand must meet the hours hand..

angle covered by hours hand = 360 / 12 = 30 deg / hour = 1/2 deg /minutes

angle covered by minutes hand = 360/ 60 min = 6 deg / min.

Let us say that the two hands meet after a period of T minutes.

1/2 * T = 6 * T - 360

11 T /2 = 360 T = 720/11 = 65 min + 5/11 minutes

in 24 hours, 24 * 60 / T = 24 * 60 * 11 / 720 = 22 times they meet

The minutes hand turns 360 degrees in one hour. So in one hour the minutes hand must meet the hours hand..

angle covered by hours hand = 360 / 12 = 30 deg / hour = 1/2 deg /minutes

angle covered by minutes hand = 360/ 60 min = 6 deg / min.

Let us say that the two hands meet after a period of T minutes.

1/2 * T = 6 * T - 360

11 T /2 = 360 T = 720/11 = 65 min + 5/11 minutes

in 24 hours, 24 * 60 / T = 24 * 60 * 11 / 720 = 22 times they meet