Question

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). If it takes 9 hours to empty a tank of water when the pumping rate is 60 gallons per hour, how long does it take to empty the tank when the pumping rate is 180 gallons per hour?

Answer 1

It takes 3 hours to empty the tank when the pumping rate is 180 gallons per hour.

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).

`t=(k)/(r)`

where k is a constant.

It takes 9 hours to empty a tank of water when the pumping rate is 60 gallons per hour.

`9=(k)/(60)\\\\k=540gallons`

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

`t=(k)/(r)\\\\t=(540)/(180)\\\\t=3hours`

It takes 3 hours to empty the tank when the pumping rate is 180 gallons per hour.