Question 277234
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V can make a cookie in 7 minutes, so it stands to reason that he can make *[tex \Large \frac{1}{7}]th of a cookie in one minute.  Likewise, S can make *[tex \Large \frac{1}{12}]th of a cookie in one minute, but L subtracts *[tex \Large  \frac{1}{9}]th of a cookie each minute.


All three working together (or against one another in the case of L) make:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{1}{7}\ +\ \frac{1}{12}\ -\ \frac{1}{9}]


cookies in one minute.


But then we can say that working together the three can make a single cookie in


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{1}{\frac{1}{7}\ +\ \frac{1}{12}\ -\ \frac{1}{9}}]


minutes.  Calculate that mess and then multiply by 500 to get the amount of time for 500 cookies, then divide that result by 60 to get the number of hours.


Warning!  The fractions in this problem, because of the fact that the given numbers of minutes are all co-prime, are uglier than a mud fence.  Be prepared to round off your decimal fractions at the end.


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