What time is it if the second hand is exactly on a second mark, and exactly 18 second marks ahead of the hour hand?

The Hour hand completes a full circuit in 12 hours. It is exactly on a second/minute mark every 12/60 hrs or every 12 minutes. Since it is an exact number of minutes, the second hand must have returned to where it was at noon (or midnight), that is, at the top mark.

The hour hand is 18 marks behind the second hand, which represents 18 x 12 minutes = 216 minutes = 3 hours, 36 minutes.

3 hours 36minutes before 12:00 is 8:24:00

As a check, 18 minutes before the hour is 42 minutes after the previous hour. At such a time, the minute hand would be two marks past the mark that corresponds to the 8:00 hour mark. The hour hand will reach that same mark 24 minutes after it reaches the 8:00 mark.

Posted by TomM on 2005-06-19 15:45:20