document.write( "Question 1117661: Please help me solve this equation:\r
\n" ); document.write( "\n" ); document.write( "The hour and minute of a watch are exactly together between 8 and 9 o'clock; required the time\r
\n" ); document.write( "\n" ); document.write( "I don't understand how to work this problem. I can't show my work because I wasn't able to work the problem at all.\r
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Algebra.Com's Answer #732774 by ikleyn(52830) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "I will count and compare the angles that the hour hand and the minute hand make with the direction \"vertically up\", \r\n" );
document.write( "which is their position at noon.\r\n" );
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document.write( "The hour hand rotates 360 degs in 12 hours; hence, its angular velocity is  = 0.5 degree per minute.\r\n" );
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document.write( "The minute hand rotates  = 6 degrees per minute; it is its angular velocity.\r\n" );
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document.write( "Let the current time is  8 hours and t minutes,  0 <= t <= 60.\r\n" );
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document.write( "The position of the hour hand is 8*30 + 0.5*t  degrees (counting from the direction \"vertically up\")).\r\n" );
document.write( "The position of the minute hand is  6t degrees.\r\n" );
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document.write( "The positions coincide - it gives you an equation\r\n" );
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document.write( "    8*30 + 0.5t = 6t.\r\n" );
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document.write( "Simplify and solve for t:\r\n" );
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document.write( "    240 = 6t - 0.5t  ====>  5.5t = 240  ====>  t =  = 43.6363 . . . minutes = 43 minutes and 38 seconds.\r\n" );
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document.write( "Answer.  The time is  8 hours 43 minutes and 38 seconds.\r\n" );
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\n" ); document.write( "To see many other similar solved problems, look into the lesson\r
\n" ); document.write( "\n" ); document.write( " - Clock problems \r
\n" ); document.write( "\n" ); document.write( " - Advanced clock problems\r
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