A water tank can be filled by an inlet pipe in

6 hours. It takes
3 times as long for the outlet pipe to empty the tank. How long will it take to fill the tank if both pipes are open?

To solve this problem, we need to determine the filling and emptying rates of the inlet and outlet pipes, respectively.

Let's say the filling rate of the inlet pipe is x tanks per hour. Since it can fill the tank in 6 hours, we can write the equation:

6x = 1 tank

This means that the inlet pipe can fill 1 tank in 6 hours, so the rate would be 1/6 tanks per hour.

Now, the outlet pipe takes 3 times as long to empty the tank. If we let the emptying rate of the outlet pipe be y tanks per hour, we can write the equation:

3y = 1 tank

This means that the outlet pipe can empty 1 tank in 3 hours, so the rate would be 1/3 tanks per hour.

To find how long it will take to fill the tank if both pipes are open, we need to find the combined rate of both pipes. Since they're working together, we can add their rates:

Combined rate = Inlet pipe rate + Outlet pipe rate
Combined rate = 1/6 + 1/3 tanks per hour
Combined rate = 1/6 + 2/6 tanks per hour
Combined rate = 3/6 tanks per hour
Combined rate = 1/2 tanks per hour

Now, to find the time it takes to fill the tank if both pipes are open, we can use the formula:

Time = Amount / Rate

Since we want to fill the tank (which has a capacity of 1 tank), we plug in the values into the formula:

Time = 1 tank / (1/2 tanks per hour)
Time = 1 tank * (2 tanks per hour)
Time = 2 hours

Therefore, it will take 2 hours to fill the tank if both pipes are open.

1/6 - 1/18 = 1/x

x = 9