At what time between 2 o'clock and 3 o’clock will the hour and minute hands of a clock be 12 minutes division apart?

To find when the hands are 12 minute divisions apart between 2 and 3 o'clock, we use the relative speed of the hands. At 2:00, the minute hand is at 0 and the hour hand is at 10 minute divisions (since each hour represents 5 divisions). The minute hand moves at 6° per minute, while the hour hand moves at 0.5° per minute, resulting in a relative speed of 5.5° per minute or 11/12 minute divisions per minute. For the hands to be 12 divisions apart, the minute hand must either be 12 divisions behind or 12 divisions ahead of the hour hand. Since it starts 10 divisions behind, being 12 divisions ahead requires gaining 10 + 12 = 22 divisions. Using the formula: Time = Distance / Relative Speed, we get 22 / (11/12) = 24 minutes. Thus, at 24 minutes past 2 o'clock, they are 12 divisions apart.