This is not a hw question. It is a question my sister asked me, and although I could solve it, I could not explain some parts of the solution.(adsbygoogle = window.adsbygoogle || []).push({});

The question is:

John and Mary are working on a job together. If John does it alone, it will take him 7 days, while Mary can do it alone in 5 days. How long will it take them to do it together?

I know that you set up [itex]\frac{1}{7}[/itex]+[itex]\frac{1}{5}[/itex]=[itex]\frac{1}{x}[/itex]

I know that the denominators all represent total time it takes to do the job.

Thus the x value in the denominator represents the total time it takes for both John and Mary to complete the job together.

I know how to solve for x algebraically, no problem there.

The part that confuses me what the numerator is supposed to represent. For instance, is it:

[itex]\frac{1 job}{7 days}[/itex]+[itex]\frac{1 job}{5 days}[/itex]=[itex]\frac{1 job}{x days}[/itex] or [itex]\frac{1 day worked}{7 total days}[/itex]+[itex]\frac{1 day worked}{5 total days}[/itex]=[itex]\frac{1 day worked}{x total days}[/itex]

What "unit" or "thing" does the numerator of this rate statement represent? Are one of these guesses correct or is it something completely different?

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# Classic combined rates of work word Problem

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