Question 202365
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With the given information, you can see that


Sam can do *[tex \Large \frac{1}{16}\text{th}] of the job in one day,


Angela can do *[tex \Large \frac{1}{24}\text{th}] of the job in one day,


Beth can do *[tex \Large \frac{1}{48}\text{th}] of the job in one day, and


Ryan can do *[tex \Large \frac{1}{12}\text{th}] of the job in one day.


The first day, Sam and Angela do:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{1}{16}+\frac{1}{24}\ =\ \frac{3}{48}+\frac{2}{48}\ =\ \frac{5}{48}\text{ths}] of the whole job.


Then next day, Angela and Beth do:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{1}{24}+\frac{1}{48}\ =\ \frac{2}{48}+\frac{1}{48}\ =\ \frac{3}{48}\text{ths}] of the whole job.


Which, added to the previous days work:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{5}{48}+\frac{3}{48}\ =\ \frac{8}{48}\text{ths}] of the job completed by the end of the 2nd day.


Continuing:


Beth and Sam manage:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{1}{48}+\frac{1}{16}\ =\ \frac{1}{48}+\frac{3}{48}\ =\ \frac{4}{48}\text{ths}] of the whole job.


And then


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{8}{48}+\frac{4}{48}\ =\ \frac{12}{48}\text{ths}] of the job completed by the end of the 3rd day.


Ryan by himself:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{1}{12}\ =\ \frac{4}{48}\text{ths}] of the whole job.


And then


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{12}{48}+\frac{4}{48}\ =\ \frac{16}{48}\text{ths}] of the job completed by the end of the 4rd day.


But *[tex \Large \frac{16}{48}\ =\ \frac{1}{3}], so in one 4-day cycle, one-third of the entire job is complete.  Hence it will take three 4-day cycles, or 12 days to complete the job.


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