Question 193360
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Working together, they can do the job in 6 hours which means that they can do *[tex \LARGE \frac{1}{6}] of the job in 1 hour. Let <b><i>x</i></b> represent the number of hours it would take Bill to do the entire job by himself.  Then he can do *[tex \LARGE \frac{1}{x}] of the job in one hour.  Likewise, Jeff can do *[tex \LARGE \frac{1}{x + 5}] of the job in one hour, and together they can do *[tex \LARGE \frac{1}{x} + \frac{1}{x + 5} = \frac {2x + 5}{x^2 + 5x} ] of the job in 1 hour.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac {2x + 5}{x^2 + 5x} = \frac{1}{6}]


Cross multiply and put the resulting quadratic into standard form:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x^2 - 7x - 30 = 0]


Factor and solve.  Exclude the negative root as extraneous.


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