Let 1/A be the fraction of the house Andy can paint in an hour, that is to say Andy can paint the entire house in A hours. Similarly 1/C for Charlotte, 1/N for Nancy.
3.5((1/A)+(1/C))=1
4.0((1/C)+(1/N))=1
3.0((1/A)+(1/C)+(1/N))=1
The most natural way is to solve for the reciprocals.
1/A+1/C =1/3.5=2/7
1/C+1/N =1/4
1/A+1/C+1/N =1/3
Third equation minus second equation gives
1/A=1/3-1/4=1/12 A=12
First equation now reads
1/12+1/C=2/7 or 1/C=2/7-1/12=(24-7)/84=17/84 C=84/17
Second equation now reads
17/84+1/N=21/84 or 1/N=4/84=1/21 or N=21
1/12+17/84=24/84=2/7
17/84+4/84=21/84=1/4
1/12+17/84+1/21=(7+17+4)/84=28/84=1/3
Michael F.
tutor
C=84/17 so Charlotte ca paint the house in 84/17 hours. 4 16/17 hrs
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04/27/14
Christy W.
Where did you get 2/7 in the first equation?
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04/27/14
Jim S.
tutor
Christy,
I have worked this problem in a different way. By the time I got around to putting the answer up Michael F had already solved the problem. If you are still confused let me know and I'll input my approach. I got the same answer it's just a different way of formulating the equations.
Jim
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04/27/14
Christy W.
Jim yes I would very much like to see how you went about this problem.
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04/27/14
Michael F.
tutor
Christy, the 2/7 is the fraction of the house done each hour, if the whole house takes 3.5 hours. 2/7=1/3.5
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04/28/14
Christy W.
04/26/14