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32 votes
32 votes
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

User Meneghino
by
3.1k points

1 Answer

18 votes
18 votes

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(\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(\rm gal)/(\rm min)\right) \implies t = \boxed{27\,\mathrm{min}}

User Shmuelp
by
3.2k points