document.write( "Question 198523: A can do a piece of work in 18 days and B can do it in 21 days. A, B, and C together can finish the work in 7 days. How long will it take C alone to finish the work? \n" ); document.write( "

Algebra.Com's Answer #149045 by Edwin McCravy(20055) $\"\"$ $\"About$

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A can do a piece of work in 18 days and B can do it in 21 days. A, B, and C together can finish the work in 7 days. How long will it take C alone to finish the work?
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document.write( "Let x be the number of days C to finish the work.\r\n" );
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document.write( "Make this chart, filling in 1's for the number of pieces of work,\r\n" );
document.write( "since exactly 1 was done in each case.  Then fill in the given\r\n" );
document.write( "times and the unknown time x for C\r\n" );
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document.write( "        PIECES OF WORK  =    RATE  * TIME\r\n" );
document.write( "A             1                       18\r\n" );
document.write( "B             1                       21\r\n" );
document.write( "C             1                        x\r\n" );
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document.write( "A&B&C         1                        7\r\n" );
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document.write( "        \r\n" );
document.write( "Now we fill in the rates in pieces of work per day,\r\n" );
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document.write( "using \r\n" );
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document.write( "        PIECES OF WORK  =    RATE  * TIME\r\n" );
document.write( "A             1              1/18     18\r\n" );
document.write( "B             1              1/21     21\r\n" );
document.write( "C             1               1/x      x\r\n" );
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document.write( "A&B&C         1               1/7      7\r\n" );
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document.write( "So we add up the rates of A, B, and C and that must equal\r\n" );
document.write( "to their combined rate. We get it all from the middle\r\n" );
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document.write( "Can you solve that for x?  Answer: days. \r\n" );
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document.write( "Edwin

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