Question 381909
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Let *[tex \Large x] be the number of hours worker A takes to do the job by himself.  Then *[tex \Large x\ -\ 3] is the time it takes worker B, the faster worker.


If A can do the job in *[tex \Large x] hours, he can do *[tex \Large \frac{1}{x}] of the job in one hour.  Likewise B can do *[tex \Large \frac{1}{x\ -\ 3}] of the job in 1 hour.  Working together they can do:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{1}{x}\ +\ \frac{1}{x\ -\ 3}]


of the job in one hour.  But we also know that working together they can do *[tex \Large \frac{1}{9}] of the job in one hour, so:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{1}{x}\ +\ \frac{1}{x\ -\ 3}\ =\ \frac{1}{9}]


Just solve for *[tex \Large x] to determine the time for A to do the job by himself and then subtract 3 to get how long it takes B to do it herself.  The quadratic equation that you will have to solve does NOT factor, so use the quadratic formula.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
My calculator said it, I believe it, that settles it
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