document.write( "Question 1195550: It is now between 10:00-11:00 o'clock, and six minutes from now, the minute hand of a watch will be exactly opposite the place where the hour hand was three minutes ago. What is the exact time now? \n" ); document.write( "

Algebra.Com's Answer #828075 by ikleyn(52790) $\"\"$ $\"About$

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\n" ); document.write( "It is now between 10:00-11:00 o'clock, and six minutes from now,
\n" ); document.write( "the minute hand of a watch will be exactly opposite the place where the hour hand
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document.write( "Imagine wall clock and its clock face.\r\n" );
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document.write( "I will measure degrees in clockwise direction, starting from position 12:00 \r\n" );
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document.write( "Let \"m\" be the number of minutes after 10:00 under the problem's question\r\n" );
document.write( "(notice that under this consideration, \"m\" is not necessary integer number: it can be a real number, actually).\r\n" );
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document.write( "The angle for the hour hand 3 minutes ago from now was  300 +  = 300 +  degrees.\r\n" );
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document.write( "The angle for the minute hand 6 minutes from now will be   degrees = 6(m+6) degrees.\r\n" );
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document.write( "Our equation to find \"m\" is\r\n" );
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document.write( "    300 +  = 180 + 6(m+6).\r\n" );
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document.write( "Simplify\r\n" );
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document.write( "    600 - 360   = 12(m+6) - (m-3)\r\n" );
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document.write( "       240      = 12m + 72 - m + 3\r\n" );
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document.write( "       240      = 11m + 75\r\n" );
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document.write( "       240 - 75 = 11m\r\n" );
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document.write( "          165   = 11m\r\n" );
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document.write( "           m    = 165/11 = 15 minutes.\r\n" );
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document.write( "ANSWER  to the problem's question is  15 minutes after 10:00,  or  10:15.\r\n" );
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\n" ); document.write( "\n" ); document.write( "To see many other similar and different clock hand 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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