document.write( "Question 1163942: there is a clock. The long and short hands are on a straight line. How long does it take for the 2 hands to overlap. \n" ); document.write( "

Algebra.Com's Answer #788196 by ikleyn(52879) $\"\"$ $\"About$

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\n" ); document.write( "there is a clock. The long and short hands are on a straight line $\"highlight%28in_opposite_directions%29\"$ .
\n" ); document.write( "How long does it take for the 2 hands to overlap.
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document.write( "It is clear that the answer is the same for any possible positions of the two hands satisfying the given condition.\r\n" );
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document.write( "Therefore, let's assume that the initial position of the hands is 6:00 PM.\r\n" );
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document.write( "The minute hand is in position 90° vertically up.\r\n" );
document.write( "The hour hand is in position -90° vertically down.\r\n" );
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document.write( "The angular speed of the minute hand is 360° per hour, or   = 6 degrees per minute.\r\n" );
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document.write( "The angular speed of the hour   hand is 360° per 12 hours, or   =  = 0.5 degrees per minute.\r\n" );
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document.write( "The position of the minute hand t minutes after 6:00 pm is  90 - 6t  degrees.\r\n" );
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document.write( "The position of the hour   hand t minutes after 6:00 pm is  -90 - 0.5t  degrees.\r\n" );
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document.write( "The hands overlap means\r\n" );
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document.write( "    90 - 6t = -90 - 0.5t,   or\r\n" );
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document.write( "    90 + 90 = 6t - 0.5t\r\n" );
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document.write( "    180     = 5.5t\r\n" );
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document.write( "    t       =  =  = 32.7272... minutes = 32 minutes 43.632 seconds, or approximately 32 minutes and 44 seconds.\r\n" );
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document.write( "So, the answer to the problem's question is   minutes, or 32 minutes and 44 seconds.\r\n" );
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\n" ); document.write( "\n" ); document.write( "To see many other similar solved problems, look into the lessons\r
\n" ); document.write( "\n" ); document.write( " - Clock problems \r
\n" ); document.write( "\n" ); document.write( " - Advanced clock problems\r
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