Question 1186342
<br>
The normal angular speed for the hour hand is 30 degrees per hour, clockwise of course.  So starting at 12:00 noon this clock's hour hand starts moving at 60 degrees per hour, still clockwise.<br>
The normal angular speed for the minute hand is 360 degrees per hour, clockwise.  So starting at 12:00 noon this clock's minute hand starts moving at 180 degrees per hour, counterclockwise.<br>
For the hands to meet after 12:00, the two hands need to move a total of 360 degrees.<br>
Let t be the number of hours after 12:00 where the hands meet again.<br>
60t+180t=360
240t=360
t=360/240=3/2 or 1.5<br>
ANSWER: It will take 1.5 hours starting at 12:00 for the two hands to meet again; so the correct time will be 1:30pm.<br>