Question 620951
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I think for this one I would calculate the time to fill the entire pool, then take 2/3 of that.


If it takes 32 hours to fill the pool with the inlet, then the inlet can fill *[tex \LARGE \frac{1}{32}] of the pool in one hour.  Likewise, the drain can empty *[tex \LARGE \frac{1}{48}] of the pool in one hour.  With both valves open, the pool will fill (fill because *[tex \LARGE \frac{1}{32}\ >\ \frac{1}{48}]) at a rate of *[tex \LARGE \frac{1}{32}\ -\ \frac{1}{48}\ =\ \frac{3}{96}\ -\ \frac{2}{96}\ =\ \frac{1}{96}] of the pool in 1 hour, so working against one another the entire pool would fill in 96 hours.


So to fill *[tex \LARGE \frac{2}{3}] of the pool it would take *[tex \LARGE \frac{2}{3}\,\cdot\,96\ =\ 64] hours.


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it
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