document.write( "Question 327804: John takes 3 hours longer than Andrew to
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Algebra.Com's Answer #234768 by Edwin McCravy(20056) $\"\"$ $\"About$

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John takes 3 hours longer than Andrew to
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document.write( "This is a slightly different approach. The other tutor added\r\n" );
document.write( "up fractions of a job in one hour.  I take it from a rate\r\n" );
document.write( "approach, whene their rate together equals the sum of their\r\n" );
document.write( "individual rates.  Either way is correct.  I just prefer this\r\n" );
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document.write( "Make this chart\r\n" );
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document.write( "               Number of      Time       Rate  \r\n" );
document.write( "               batches of      in         in\r\n" );
document.write( "                apples        hours    batches/hr  \r\n" );
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document.write( "John alone         \r\n" );
document.write( "Andrew alone       \r\n" );
document.write( "Both together     \r\n" );
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document.write( "Let Andrew's time working alone be x.  We fill that in:\r\n" );
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document.write( "               Number of      Time       Rate  \r\n" );
document.write( "               batches of      in         in\r\n" );
document.write( "                apples        hours    batches/hr\r\n" );
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document.write( "John alone        \r\n" );
document.write( "Andrew alone                    x        \r\n" );
document.write( "Both together                   \r\n" );
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document.write( ">>...John takes 3 hours longer than Andrew...<<\r\n" );
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document.write( "So John's time working alone is x+3, so we fill that in.\r\n" );
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document.write( "               Number of      Time       Rate  \r\n" );
document.write( "               batches of      in         in\r\n" );
document.write( "                apples        hours    batches/hr  \r\n" );
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document.write( "John alone                     x+3       \r\n" );
document.write( "Andrew alone                    x        \r\n" );
document.write( "Both together                         \r\n" );
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document.write( ">>...together they can peel 500 lb of apples in 8 hours...<<\r\n" );
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document.write( "So we fill that in for the time for both together:\r\n" );
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document.write( "               Number of      Time       Rate  \r\n" );
document.write( "               batches of      in         in\r\n" );
document.write( "                apples        hours    batches/hr  \r\n" );
document.write( "-------------------------------------------------\r\n" );
document.write( "John alone                     x+3       \r\n" );
document.write( "Andrew alone                    x        \r\n" );
document.write( "Both together                   8        \r\n" );
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document.write( "In all three cases exactly 1 batch (500 lbs) of apples are peeled. \r\n" );
document.write( "So we put 1's for the number of batches of apples peeled. \r\n" );
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document.write( "               Number of      Time       Rate  \r\n" );
document.write( "               batches of      in         in\r\n" );
document.write( "                apples        hours    batches/hr  \r\n" );
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document.write( "John alone         1           x+3       \r\n" );
document.write( "Andrew alone       1            x        \r\n" );
document.write( "Both together      1            8        \r\n" );
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document.write( "Now we form the three rates by Rate = \r\n" );
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document.write( "               Number of      Time       Rate  \r\n" );
document.write( "               batches of      in         in\r\n" );
document.write( "                apples        hours    batches/hr \r\n" );
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document.write( "John alone         1           x+3       1/(x+3)\r\n" );
document.write( "Andrew alone       1            x        1/x\r\n" );
document.write( "Both together      1            8        1/8\r\n" );
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document.write( "Now we make the equation by:\r\n" );
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document.write( "         John's alone rate + Andrew's rate alone = Rate of both together\r\n" );
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document.write( "               1/(x+3)     +        1/x          =         1/8\r\n" );
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document.write( "Can you solve that by first getting the LCD? If not post again asking how.\r\n" );
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document.write( "Solution:  .\r\n" );
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document.write( "Those two solutions are approximately \r\n" );
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document.write( " and \r\n" );
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document.write( "We ignore the negative answer and conclude that Andrew's time\r\n" );
document.write( "alone is about 14.6 hours and since John takes 3 hours longer,\r\n" );
document.write( "or about 14.6 + 3 = 17.6 hours.\r\n" );
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document.write( "Edwin

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