<PRE><B>Question 272869</B>
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Without knowing specifically how long it takes either one of the participants to do the entire job (or some specified portion of the job) all you can tell is the proportional difference between the amount of time it would take &lt;b&gt;&lt;i&gt;j&lt;/i&gt;&lt;/b&gt; working alone vs. &lt;b&gt;&lt;i&gt;c&lt;/i&gt;&lt;/b&gt; working alone vs. the two of them working together.


Let *[tex \Large x] represent the number of time periods it would take &lt;b&gt;&lt;i&gt;c&lt;/i&gt;&lt;/b&gt; working alone.  Then *[tex \Large 3x] represents the number of time periods it would take &lt;b&gt;&lt;i&gt;j&lt;/i&gt;&lt;/b&gt; working alone.


&lt;b&gt;&lt;i&gt;c&lt;/i&gt;&lt;/b&gt; can do *[tex \Large \frac{1}{x}] of the job in one time period.  Likewise, &lt;b&gt;&lt;i&gt;j&lt;/i&gt;&lt;/b&gt; can do *[tex \Large \frac{1}{3x}] of the job in one time period.  Then, working together they can do:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{1}{x}\ +\ \frac{1}{3x}\ =\ \frac{4}{3x}]


of the job in one time period.  Hence, they would take:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{3x}{4}] time periods to do the entire job.


So, however long it takes &lt;b&gt;&lt;i&gt;c&lt;/i&gt;&lt;/b&gt; to do the entire job by herself is the value of *[tex \Large x] and three-fourths of that is the time it would take the two of them working together.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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