document.write( "Question 1185859: How many minutes after five o’clock will the hands of the clock be perpendicular for the second time? \n" ); document.write( "

Algebra.Com's Answer #816724 by Edwin McCravy(20055) $\"\"$ $\"About$

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document.write( "The minute hand's angular speed is 360 degrees per hour. or 6 degrees per minute\r\n" );
document.write( "The hour hand's angular speed is 360 degrees per 12 hours, which is equal to\r\n" );
document.write( "30 degrees per hour, or 0.5 degrees per minute.  The angle between the hands is\r\n" );
document.write( "either decreasing or increasing at the rate of 6-0.5 = 5.5 degrees per minute.\r\n" );
document.write( "At 5 o'clock the angle between the hands is 150 degrees. The angle between the\r\n" );
document.write( "hands is decreasing at 5.5 degrees per minute.   The hands will be together when\r\n" );
document.write( "the angle between them decreases the entire 150 degrees to 0. That will be\r\n" );
document.write( "150/5.5 = 27 3/11 minutes. [Notice that on the hands' way to being together from\r\n" );
document.write( "5 o'clock, they were perpendicular at one instant.]  Then after the hands are\r\n" );
document.write( "together, the angle between the hands begins increasing at 5.5 degrees per\r\n" );
document.write( "minute. They will be 90 degrees apart in 90/5.5 = 16 4/11 minutes.  That will be\r\n" );
document.write( "the second time after five o'clock they were perpendicular.  So the answer is\r\n" );
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document.write( "27 3/11 + 16 4/11 = 43 7/ll minutes.  \r\n" );
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document.write( "Edwin

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