Question

The time t required to empty a tank varies inversely as

Answer 1

If $t$ and $r$ are inverse proportional to one another, then for some constant volume $V$ we have

$V = tr$

It takes 45 min to empty a tank containing at 300 gal/min, so the tank contains

$V = (45\,\mathrm{min}) \left(300\dfrac{\rm gal}{\rm min}\right) = 13500\,\mathrm{gal}$

of liquid.

If it's emptied at 500 gal/min, it would take

$13500\,\mathrm{gal} = t \left(500\dfrac{\rm gal}{\rm min}\right) \implies t = \boxed{27\,\mathrm{min}}$