document.write( "Question 639534: If a guy can wash a car in 6 minutes by himself and a different guy can wash the car in 8 minutes by himself how long would it take to wash the car together \n" ); document.write( "

Algebra.Com's Answer #402792 by Edwin McCravy(20054) $\"\"$ $\"About$

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If a guy can wash a car in 6 minutes by himself and a different guy can wash the car in 8 minutes by himself how long would it take to wash the car together.\r
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document.write( "There are two methods, (1) in your head and (2) by algebra.\r\n" );
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document.write( "(1) In your head.\r\n" );
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document.write( "The LCM of 6 minutes and 8 minutes is 24 minutes.  Working together for 24 minutes, \r\n" );
document.write( "washing identical cars, the first guy would wash 4 cars and the second\r\n" );
document.write( "guy would wash 3 cars.  That's 7 cars in 24 minutes or 1 car in 24/7 or  minutes.\r\n" );
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document.write( "(2)  By algebra.\r\n" );
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document.write( "Make this chart:\r\n" );
document.write( "                             Number of         No. of      Rate in  \r\n" );
document.write( "                           cars washed         Minutes     Cars/minute\r\n" );
document.write( "1st guy washing alone\r\n" );
document.write( "2nd guy washing alone\r\n" );
document.write( "Both painting together\r\n" );
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document.write( "Let x be the number of minutes required for both to wash 1 car, so fill in\r\n" );
document.write( "1 for the number of cars washed by both washing together and x for the\r\n" );
document.write( "number of minutes.  Also fill in 1 car and 6 and 8 for the numbers of minutes\r\n" );
document.write( "required for each to wash 1 car separately:\r\n" );
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document.write( "                             Number of         No. of      Rate in  \r\n" );
document.write( "                           cars washed         Minutes     Cars/minute\r\n" );
document.write( "1st guy washing alone           1                 6\r\n" );
document.write( "2nd guy washing alone           1                 8\r\n" );
document.write( "Both painting together          1                 x\r\n" );
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document.write( "Now fill in the Rates in cars/minute by dividing cars by minutes:\r\n" );
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document.write( "                             Number of         No. of      Rate in  \r\n" );
document.write( "                           cars washed         Minutes     Cars/minute\r\n" );
document.write( "1st guy washing alone           1                 6           1/6\r\n" );
document.write( "2nd guy washing alone           1                 8           1/8\r\n" );
document.write( "Both painting together          1                 x           1/x\r\n" );
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document.write( "                     The equation comes from\r\n" );
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document.write( "       +  = \r\n" );
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document.write( "                     +  = \r\n" );
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document.write( " Multiply through by 24x\r\n" );
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document.write( "                    4x + 3x = 24\r\n" );
document.write( "                         7x = 24\r\n" );
document.write( "                          x =  =  minutes.\r\n" );
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document.write( "Edwin

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