Question 179867
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Emptying the tank takes 30 minutes.  That means that the drain pipe can do *[tex \Large \frac {1}{30}\text{th}] of the job of emptying the tank in one minute.


Similarly, the fill pipe can do *[tex \Large \frac {1}{45}\text{th}]  of the job of emptying the tank in one minute.


Working against one another, the tank will empty at a rate of *[tex \Large \left(\frac {1}{30} - \frac {1}{45}\right)\text{th}] of the tank per minute.  (We know it is emptying because *[tex \Large \frac {1}{30}] is larger than *[tex \Large \frac {1}{45}])


*[tex \Large \frac {1}{30} - \frac {1}{45} = \frac {3}{90} - \frac {2}{90} = \frac {1}{90}]


So if *[tex \Large \frac {1}{90}\text{th}] of the tank empties in one minute, it takes 90 minutes to empty the whole tank.


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