document.write( "Question 1092286: It is now past 3 o'clock in the afternoon. The minute hand 3 minutes from now will be directly opposite the hour hand 9 minutes ago. What time is it? \n" ); document.write( "

Algebra.Com's Answer #706913 by ikleyn(52816) $\"\"$ $\"About$

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document.write( "Let the current time under the question be 3 hours and \"t\" minutes, where t is the real number, so t can be fraction of minutes and seconds.\r\n" );
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document.write( "The minute hand is at angular position  of   = 6t degrees, counting from its position \"vertically up\" at 3:00 pm.\r\n" );
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document.write( "     *** Minute hand makes its full revolution of  360 degrees in 60 minutes. ***\r\n" );
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document.write( "The hour hand at this moment is at the angular position   degrees, counting from its position \"vertically up\" at noon.\r\n" );
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document.write( "     *** Hour hand has the angular velocity 12 times less than the minute hand: it is 12 times slower. ***\r\n" );
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document.write( "Three minutes from now the minute hand will be in position of    degrees.\r\n" );
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document.write( "Nine minutes ago the hour hand was in position of    degrees.\r\n" );
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document.write( "Therefore, the governing equation is \r\n" );
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document.write( " =  + 180  degrees.\r\n" );
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document.write( "          The major part is done: the equation/the model is set up.\r\n" );
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document.write( "          The rest is just arithmetic. \r\n" );
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document.write( "Simplify this equation\r\n" );
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document.write( "6t + 18 =   ====>\r\n" );
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document.write( " =   ====>   =   =  ====>\r\n" );
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document.write( "t =  = 45 minutes\r\n" );
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\n" ); document.write( "\n" ); document.write( "Answer. The current time is 3:45 pm.\r
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