Question 1186342
At exactly 12 o’clock noon the hour hand of a clock begins to move at twice its
normal speed, and the minute hand begins to move backward at half its normal
speed. When the two hands next coincide, what will be the correct time?
<pre>
A normal hour hand moves 360 degrees in 12 hours or 30 degrees per hour.
A normal minute hand moves 360 degrees per hour.

On this abnormal clock, beginning at noon, the hour hand moves clockwise at 60
degree per hour.  

On this abnormal clock, beginning at noon, the minute hand moves counter-
clockwise at 180 degrees per hour.

At noon the hands are together and can be considered to be either 0 degrees or
360 degrees apart.  At noon, the angle between the hands begins decreasing from
360 degrees at the rate of the sum of their speeds (because the hands are
approaching each other), which is 180+60=240 degrees per hour. The angle between
them will decrease from 360 degrees to 0 degrees in 360/240 = 1.5 hours, which
will be at 1:30 PM.

Edwin</pre>