document.write( "Question 777842: At how many minutes after 5 PM will the hands of a clock become perpendicular for the first time? \n" ); document.write( "

Algebra.Com's Answer #474298 by Edwin McCravy(20054) $\"\"$ $\"About$

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At how many minutes after 5 PM will the hands of a clock become perpendicular for the first time?
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document.write( "The angular speed of the minute hand is 360° per hour or 6° per minute.\r\n" );
document.write( "The angular speed of the hour hand is 360° per 12 hours or 30° per hour,\r\n" );
document.write( "or 1/2 a degree or 0.5° per minute.\r\n" );
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document.write( "The catch-up rate of the minute hand to the hour hand in the vicinity \r\n" );
document.write( "of 5 PM is the difference in their angular speeds or 6°-0.5° or 5.5° \r\n" );
document.write( "per minute.\r\n" );
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document.write( "That is, in the vicinity of 5 PM the angle between the two hands is \r\n" );
document.write( "shrinking at the rate of 5.5° per minute. \r\n" );
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document.write( "At 5 PM the hour hand is 5/12ths of 360° or 150° ahead of the minute hand.\r\n" );
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document.write( "We want to find when the hour hand will have shrunk from 150° down to\r\n" );
document.write( "90°, which is a decrease of 60°.\r\n" );
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document.write( "Answer:  time = angle/rate = 60°/5.5° = 600/55 = 120/11 = 10 10/11 minutes.\r\n" );
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document.write( "Edwin

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