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September 20th, 2014, 06:23 PM   #1
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Rate of Work (Linear Systems)

Hey guys! I'm new to this forum and I really need help with this problem.

"Working alone, Mary can complete a certain job in 8h. If Mary and Paul work together, they can complete the same job in 6h. If Peter and Paul together, they can complete the same job in 10h. How long would it take Peter, Paul, and Mary working together to complete the job?"

My assignment is due on Monday, and it's Saturday. Help a girl out.

Please and Thank You.
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September 20th, 2014, 08:04 PM   #2
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In 1 hour:

$\displaystyle M=\frac18$

$\displaystyle M+P_a=\frac16\Rightarrow P_a=\frac{1}{24}$

$\displaystyle P_a+P_e=\frac{1}{10}\Rightarrow P_e=\frac{7}{120}$

$\displaystyle M+P_a+P_e=\frac18+\frac{1}{24}+\frac{7}{120}=\frac {9}{40}$

Hence the job is completed in $\displaystyle \frac{40}{9}$ hours with Peter, Paul and Mary working together.
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September 20th, 2014, 08:05 PM   #3
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This is about the rate of work.
Let's have $m = \frac18$ is the amount of work Mary can do in one hour, $p$ is the work that Paul can do in one hour and $q$ is the work Peter can do in an hour. Then $p+q = \frac{1}{10}$ so $m+p+q = \tfrac18 + \frac{1}{10} = \frac{18}{80} = \frac{9}{40}$. Thus the three working together would complete the job in $\frac{40}{9}$ hours or 4 hours 26 minutes and 40 seconds.

Last edited by v8archie; September 20th, 2014 at 08:07 PM.
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