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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?
Answer by oberobic(2304)   (Show Source):
You can put this solution on YOUR website! Work problems are fraction problems in disguise.
Each resource does a fraction of the work per unit of time.
All of the resource fractions total 1 whole job.
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Clarissa can do the job in 5 days less than Shawna.
But we don't now how fast Shawna can do the job.
Hmmm.
We can define Shawna as doing the job in 'S' days.
So she does 1/S of the job per day.
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Clarissa does the job in S-5 days.
So she does 1/(S-5) of the job per day.
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Working together they can do the job in 6 days.
So they can do 1/6 of the job per day.
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(1/S + 1/S-5)*6 = 1 whole job
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(S-5+S)/(S*(S-5)) = 1/6
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(2S -5)/(S^2-5S) = 1/6
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cross multiply
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6*(2S-5) = S^2 -5S
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12S -30 = S^2 -5S
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-30 = S^2 -17S
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0 = S^2 -17S + 30
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0 = (S-2)(S-15)
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So, S = 2 or S = 15.
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But we're told Clarissa can do the job 5 days faster than Shawna.
That means S=2 is a spurious root: It is algebraically correct but nonsensical.
(Compare this to a negative width or length.)
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S = 15
so
C = 10
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Check to see if this is the right answer.
Working together, can they do the whole job in 6 days?
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(1/15 + 1/10)*6 = 1 ??
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(2/30 + 3/30)*6 = (5/30)*6
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(5/30)*6 = 30/30 = 1
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Correct.
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Answer: Working alone, Clarissa can do the job in 10 days.
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How about that spurious root? Would that work out algebraically?
Let's see.
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S = 2
so
C = -3
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(1/2 + 1/-3)*6 = ??
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(3/6 - 2/6)*6 = 1/6*6 = 6/6 = 1
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Yep. But there is no way for Clarissa to the job in negative 3 days.
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Done.
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