Step-by-step explanation:
The time t (in hours) that it takes a pump to empty a tank of water varies inversely with the pumping rate r (in gallons per hour).
[tex]t=\frac{k}{r}[/tex]
where k is a constant.
It takes 9 hours to empty a tank of water when the pumping rate is 60 gallons per hour.
[tex]9=\frac{k}{60}\\\\k=540gallons[/tex]
We need to find how long does it take to empty the tank when the pumping rate is 180 gallons per hour ( r = 180)
We have
[tex]t=\frac{k}{r}\\\\t=\frac{540}{180}\\\\t=3hours[/tex]
It takes 3 hours to empty the tank when the pumping rate is 180 gallons per hour.
