document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1186342>Question 1186342</A>: <I><SPAN STYLE=\"word-break: break-all;\"> At exactly 12 o’clock noon the hour hand of a clock begins to move at twice its<BR>\n" );
document.write( "normal speed, and the minute hand begins to move backward at half its normal<BR>\n" );
document.write( "speed. When the two hands next coincide, what will be the correct time? </SPAN>\n" );
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document.write( "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><BR>\n" );
document.write( "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><BR>\n" );
document.write( "For the hands to meet after 12:00, the two hands need to move a total of 360 degrees.<br><BR>\n" );
document.write( "Let t be the number of hours after 12:00 where the hands meet again.<br><BR>\n" );
document.write( "60t+180t=360<BR>\n" );
document.write( "240t=360<BR>\n" );
document.write( "t=360/240=3/2 or 1.5<br><BR>\n" );
document.write( "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><BR>\n" );
document.write( " </SPAN>\n" );
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