Question 1117460
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If the hot water tap can fill the bathtub in 9 minutes, then the hot water tap must fill *[tex \Large \frac{1}{9}] of the bathtub in one minute.  Likewise, the cold tap fills *[tex \Large \frac{1}{12}] of the tub in one minute and the drain empties *[tex \Large \frac{1}{18}] of the tub in one minute.  So altogether:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{1}{9}\ +\ \frac{1}{12}\ -\ \frac{1}{18}]


of the tub gets filled (because this is clearly a positive number) every minute, and it will take the reciprocal of the above sum in minutes to fill the tub, so since the lowest common denominator is 36:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{4}{36}\ +\ \frac{3}{36}\ -\ \frac{2}{36}\ =\ \frac{5}{36}]


It will take *[tex \LARGE \frac{36}{5}\ =\ 7.2] minutes or 7 minutes and 12 seconds to fill the tub if both taps and the drain are open.


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it
<img src="http://c0rk.blogs.com/gr0undzer0/darwin-fish.jpg">
*[tex \Large \ \
*[tex \LARGE \ \ \ \ \ \ \ \ \ \  

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