Question 184661
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Melanie can paint a certain barn by herself in <i>x</i> days, so she can paint *[tex \Large \frac{1}{x}]th of the barn in 1 day.  Likewise her helper can paint *[tex \Large \frac{1}{2x}]th of the barn in 1 day.


Together, they can paint:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  \frac{1}{x} + \frac{1}{2x} = \frac{2 + 1}{2x} = \frac{3}{2x}]th of the barn in 1 day.


So together they take:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \ 1 \div \frac{3}{2x}=\frac{2x}{3}] days to paint the barn.


Just substitute 5 for <i>x</i> to evaluate for 5 days.


In general if A takes <i>x</i> time periods to do a job, and B takes <i>y</i> time periods to do the same job, then working together they can complete the job in:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  \frac{xy}{x + y}]


time periods.



John
*[tex \LARGE e^{i\pi} + 1 = 0]
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