Answered

The time t required to empty a tank varies inversely as
the rate r of pumping. If a pump can empty a tank in
45 minutes at a rate of 300 gallons per minute, how
long will it take to empty a tank at 500 gallons per
minute?
k

Answer :

If [tex]t[/tex] and [tex]r[/tex] are inverse proportional to one another, then for some constant volume [tex]V[/tex] we have

[tex]V = tr[/tex]

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

[tex]V = (45\,\mathrm{min}) \left(300\dfrac{\rm gal}{\rm min}\right) = 13500\,\mathrm{gal}[/tex]

of liquid.

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

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

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