between 12 o' clock and 1 o' clock, when will the hands of a clock be together again

The hands of a clock are exactly together at 12:00. The next time they will be together after 12 o'clock is not between 12 and 1 o'clock, but rather a little after 1:05. Specifically, the next overlap occurs about 1 hour, 5 and 5/11 minutes after 12 o'clock, which is approximately 1:05:27. This is because the minute hand moves faster and catches up with the hour hand only after the hour hand has moved past the 1 o'clock mark. Therefore, the hands are not together again between 12:00 and 1:00; the next coincidence is just after 1:05.