The intake pipe can fill a certain tank in 6 hours when the outlet pipe is closed, but when the outlet pipe is open it takes 9 hours. How long would it take the outlet pipe to empty a full tank?

Accepted Solution

Answer:18 hoursStep-by-step explanation:The unit rate of intake pipe is [tex]\frac{1}{6}[/tex] Β [1 tank in 6 hours]The total unit rate (combined) when 2 work together is [tex]\frac{1}{9}[/tex] Β [1 tank in 9 hours]Intake fills up and outlet empties. Thus we can say:Rate of Intake - Rate of Outlet = Combined RateThis 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