document.write( "Question 12375: A, B, and C can finish a job in 6 days. If B and C work together, the job will take 9 days; if A and C work together, the job will take 8 days. How many days will it take each man to do the job alone?\r
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Algebra.Com's Answer #6337 by AnlytcPhil(1810)\"\" \"About 
You can put this solution on YOUR website!

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document.write( "A, B, and C can finish a job in 6 days. If B and C work
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document.write( "together, the job will take 9 days; if A and C work together,
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document.write( "the job will take 8 days. How many days will it take each man
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document.write( "to do the job alone? 
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document.write( "A. A in 9 days, B in 1 day, and C in 8 days 
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document.write( "B. A in 25 days, B in 12 2/3 day, and C in 28 days 
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document.write( "C. A in 20 1/2 days, B in 16 day, and C in 25 days 
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document.write( "D. A in 18 days, B in 24 day, and C in 14 2/5 days 
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document.write( "I don't have a clue where to begin with this problem. I would
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document.write( "appreciate any help--thanks
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document.write( "Let x = the number of days it would take A to do 1 job alone.
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document.write( "Let y = the number of days it would take B to do 1 job alone.
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document.write( "Let z = the number of days it would take C to do 1 job alone.
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document.write( "Make this chart:
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document.write( "           Number of jobs | Rate(jobs/days) |  Time(days)
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document.write( "A alone                   |                 |    
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document.write( "B alone                   |                 |    
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document.write( "C alone                   |                 |    
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document.write( "A,B,& C                   |                 |     
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document.write( "B & C only                |                 |
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document.write( "A & C only                |                 |
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document.write( "In each case 1 job was done, so fill in 1 for each of the
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document.write( "numbers of jobs
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document.write( "           Number of jobs | Rate(jobs/days) |  Time(days)
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document.write( "A alone          1        |                 |    
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document.write( "B alone          1        |                 |    
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document.write( "C alone          1        |                 |    
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document.write( "A,B,& C          1        |                 |     
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document.write( "B & C only       1        |                 |
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document.write( "A & C only       1        |                 |
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document.write( "Now fill in the times (numbers of days.
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document.write( "           Number of jobs | Rate(jobs/day)  |  Time(days)
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document.write( "A alone          1        |       1/x       |      x  
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document.write( "B alone          1        |       1/y       |      y 
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document.write( "C alone          1        |       1/z       |      z
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document.write( "A,B,& C          1        |       1/6       |      6
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document.write( "B & C only       1        |       1/9       |      9
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document.write( "A & C only       1        |       1/8       |      8
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document.write( "Now fill in the rates using rate = (jobs done)/(time)
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document.write( "The rate for A,B,& C equals the sum of their individual
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document.write( "rates, which must equal 1/6, so 
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document.write( "1/x + 1/y + 1/z = 1/6
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document.write( "The rate for A & C equals the sum of their individual rates,
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document.write( "which must equal 1/8, so 
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document.write( "1/x + 1/z = 1/8
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document.write( "The rate for B & C equals the sum of their individual rates,
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document.write( "which must equal 1/9, so 
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document.write( "1/y + 1/z = 1/9
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document.write( "So we have this system of equations:
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document.write( "1/x + 1/y + 1/z = 1/6
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document.write( "1/x       + 1/z = 1/8
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document.write( "      1/y + 1/z = 1/9
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document.write( "Don't clear of fractions, but solve for 1/x, 1/y, and 1/z.
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document.write( "Can you do this system?  If not, post again and ask how to solve it.
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document.write( "You'll get 1/x = 1/18, 1/y = 1/24, and 1/z = 5/72, which
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document.write( "means x = 18 days, y = 24 days, z = 72/5 or 14 2/5 days, and the
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document.write( "correct choice is D.
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document.write( "Edwin \n" );
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