How many times are the second minute and hour hand in the exact same place?

Answer 1

Disregarding the second hand (for a few seconds), the hour and minute hands overlap (point in the same direction) 22 times in a 24 hour period. It happens once after every hour except the 12 o'clock hour. After 12 o'clock, the next occurance is after 1 o'clock. The fractions of a minute required for these overlaps do not always coincide with the number of seconds that the second hand would have to register in order for the second hand to 'join' the hour and minute hands. The only times that all three hands are perfectly overlapping (pointing in the same direction) is at 12 midnight and 12 noon. So the second minute and hour hands are in the exact same place only twice during every 24 hour period. The hour and minute hands join each other every 65.454545 minutes, or 32.727272 degrees. The minute hand advances 163.636363 degrees each time the hour and minute hands overlap.