Answer:
18 hours
Step-by-step explanation:
The unit rate of intake pipe is [tex]\frac{1}{6}[/tex] [1 tank in 6 hours]
The total unit rate (combined) when 2 work together is [tex]\frac{1}{9}[/tex] [1 tank in 9 hours]
Intake fills up and outlet empties. Thus we can say:
Rate of Intake - Rate of Outlet = Combined Rate
This becomes:
[tex]\frac{1}{6}-x=\frac{1}{9}[/tex]
Where x is the rate of outlet pipe [what we are looking for]
Doing algebra we solve for x:
[tex]\frac{1}{6}-x=\frac{1}{9}\\\frac{1}{6}-\frac{1}{9}=x\\x=\frac{9-6}{54}\\x=\frac{3}{54}[/tex]
This means "outlet pipe can empty 3 tanks in 54 hours". So that would mean 54/3 = 18 hours to empty 1 tank
