Question 219554
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Let *[tex \Large x] represent the number of hours it takes the inlet pipe to fill the tank.  Let *[tex \Large y] represent the number of hours it takes the outlet pipe to empty the tank.


If the inlet can fill the tank in *[tex \Large x] hours, it can fill *[tex \Large \frac{1}{x}] of the tank in one hour.  Likewise, the outlet can empty *[tex \Large \frac{1}{y}] of the tank in one hour.  So given both pipes open, the tank will fill at a rate of:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{1}{x}\ -\ \frac{1}{y}\ =\ \frac{y - x}{xy}] per hour.


Therefore the entire tank will be full in:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{1}{\frac{y - x}{xy}}\ =\ \frac{xy}{y-x}] hours.


Just plug in the values you were given and do the arithmetic.  Don't forget to add your answer to 8pm to get the clock time.



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