Question 275821
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If person A can complete an entire job in *[tex \Large x] time periods, then that person can complete *[tex \Large \frac{1}{x}] of the job in one time period.  Jane can do the whole job in 5 hours, so she can do *[tex \Large \frac{1}{5}] of the job in one hour.  Likewise, Paul is 6 hours and *[tex \Large \frac{1}{6}] of the job, while Peter is *[tex \Large x] hours and *[tex \Large \frac{1}{x}] of the job.  In the same way, the three of them working together can do the job in 2 hours, which is to say that the three of them working together can do *[tex \Large \frac{1}{2}] of the job in one hour.


The equation works out to "The fraction of the job that Jane can do in one hour" plus "The fraction of the job that Paul can do in one hour" plus "The fraction of the job that Peter can do in one hour" adds up to "The fraction of the job that the three of them working together can do in one hour" 



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