Question 318276
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If Annika has worked for 30 minutes on a job that would take her 2 hours, then she must have *[tex \Large \frac{3}{4}] of the job remaining and that balance must require Annika to work for *[tex \Large \frac{3}{2}] hours.  If Asa would take 3 hours to do the whole job, then she must require *[tex \Large 3\ \times\ \frac{3}{4}\ =\ \frac{9}{4}] to to the balance of the job by herself.


Now all you have to do is apply the rule for two entities working together:


If A can do a job in <i>x</i> time periods, then A can do *[tex \Large \frac{1}{x}] of the job in 1 time period.  Likewise, if B can do the same job in <i>y</i> time periods, then B can do *[tex \Large \frac{1}{y}] of the job in 1 time period.


So, working together, they can do


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  \frac{1}{x}\ +\ \frac{1}{y}\ =\ \frac{x\ +\ y}{xy} ]


of the job in 1 time period.


Therefore, they can do the whole job in:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  \frac{1}{\frac{x + y}{xy}}\ =\ \frac{xy}{x\ +\ y}]


time periods.


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