Question

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?

Answer 1

Answer:

18 hours

Step-by-step explanation:

The unit rate of intake pipe is $\frac{1}{6}$  [1 tank in 6 hours]

The total unit rate (combined) when 2 work together is $\frac{1}{9}$  [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:

$\frac{1}{6}-x=\frac{1}{9}$

Where x is the rate of outlet pipe [what we are looking for]

Doing algebra we solve for x:

$\frac{1}{6}-x=\frac{1}{9}\\\frac{1}{6}-\frac{1}{9}=x\\x=\frac{9-6}{54}\\x=\frac{3}{54}$

This means "outlet pipe can empty 3 tanks in 54 hours". So that would mean 54/3 = 18 hours to empty 1 tank