document.write( "Question 510150: Clarissa and Shawna, working together, can paint the exterior of a house in 6 days. Clarissa by herself can complete this in 5 days less than Shawna. how long will it take Clarissa to complete the job by herself? \n" ); document.write( "
Algebra.Com's Answer #341735 by oberobic(2304)\"\" \"About 
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Work problems are fraction problems in disguise.
\n" ); document.write( "Each resource does a fraction of the work per unit of time.
\n" ); document.write( "All of the resource fractions total 1 whole job.
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\n" ); document.write( "Clarissa can do the job in 5 days less than Shawna.
\n" ); document.write( "But we don't now how fast Shawna can do the job.
\n" ); document.write( "Hmmm.
\n" ); document.write( "We can define Shawna as doing the job in 'S' days.
\n" ); document.write( "So she does 1/S of the job per day.
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\n" ); document.write( "Clarissa does the job in S-5 days.
\n" ); document.write( "So she does 1/(S-5) of the job per day.
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\n" ); document.write( "Working together they can do the job in 6 days.
\n" ); document.write( "So they can do 1/6 of the job per day.
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\n" ); document.write( "(1/S + 1/S-5)*6 = 1 whole job
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\n" ); document.write( "(S-5+S)/(S*(S-5)) = 1/6
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\n" ); document.write( "(2S -5)/(S^2-5S) = 1/6
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\n" ); document.write( "cross multiply
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\n" ); document.write( "6*(2S-5) = S^2 -5S
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\n" ); document.write( "12S -30 = S^2 -5S
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\n" ); document.write( "-30 = S^2 -17S
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\n" ); document.write( "0 = S^2 -17S + 30
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\n" ); document.write( "0 = (S-2)(S-15)
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\n" ); document.write( "So, S = 2 or S = 15.
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\n" ); document.write( "But we're told Clarissa can do the job 5 days faster than Shawna.
\n" ); document.write( "That means S=2 is a spurious root: It is algebraically correct but nonsensical.
\n" ); document.write( "(Compare this to a negative width or length.)
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\n" ); document.write( "S = 15
\n" ); document.write( "so
\n" ); document.write( "C = 10
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\n" ); document.write( "Check to see if this is the right answer.
\n" ); document.write( "Working together, can they do the whole job in 6 days?
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\n" ); document.write( "(1/15 + 1/10)*6 = 1 ??
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\n" ); document.write( "(2/30 + 3/30)*6 = (5/30)*6
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\n" ); document.write( "(5/30)*6 = 30/30 = 1
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\n" ); document.write( "Correct.
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\n" ); document.write( "Answer: Working alone, Clarissa can do the job in 10 days.
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\n" ); document.write( "How about that spurious root? Would that work out algebraically?
\n" ); document.write( "Let's see.
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\n" ); document.write( "S = 2
\n" ); document.write( "so
\n" ); document.write( "C = -3
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\n" ); document.write( "(1/2 + 1/-3)*6 = ??
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\n" ); document.write( "(3/6 - 2/6)*6 = 1/6*6 = 6/6 = 1
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\n" ); document.write( "Yep. But there is no way for Clarissa to the job in negative 3 days.
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\n" ); document.write( "Done.\r
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