How Long Will It Take for an Inlet and Outlet Pipe to Fill a Tank?

Imagine you're faced with the challenge of determining how long it will take for an inlet pipe to fill a tank when it is in use alongside an outlet pipe that can empty it. This problem involves understanding the rates at which the inlet and outlet pipes work and then calculating the net effect. In this article, we will break down the process step-by-step to help you find the answer.

Let's start with the premise that an inlet pipe can fill a tank in 10 hours and an outlet pipe can empty a completely filled tank in 20 hours. Both pipes are opened at the same time, 6:30 a.m. How long will it take for the tank to get filled?

Understanding the Rates

To solve this problem, we first need to determine the rates at which the inlet and outlet pipes work.

Inlet Pipe Rate

The inlet pipe can fill the tank in 10 hours. So, the rate at which it works is:

Rate of inlet 1 tank / 10 hours 0.1 tanks per hour

Outlet Pipe Rate

The outlet pipe can empty the tank in 20 hours. Therefore, the rate at which it works is:

Rate of outlet 1 tank / 20 hours 0.05 tanks per hour

Calculating the Net Rate

When both pipes are opened simultaneously, the net rate of filling the tank is determined by subtracting the outlet rate from the inlet rate.

Net Rate

Net rate Rate of inlet - Rate of outlet 0.1 - 0.05 0.05 tanks per hour

Time to Fill the Tank

Now that we have the net rate, we can calculate the time it will take to fill the tank:

Time 1 tank / 0.05 tanks per hour 20 hours

Final Calculation

Since both pipes are opened at 6:30 a.m., the tank will be completely filled 20 hours later. Adding 20 hours to 6:30 a.m.:

6:30 a.m. 12 hours 6:30 p.m. on the same day 6:30 p.m. 8 hours 2:30 a.m. the next day

Therefore, the tank will be completely filled at 2:30 a.m. the next day.

Alternative Method

We can also use another approach to solve this problem. If both the filling and draining pipes are opened simultaneously, the time taken to completely fill the tank can be calculated as:

Time 10 x 20 / (20 - 10) 200 / 10 20 hours.

Thus, the tank will be filled at 6:30 a.m. 20 hours 2:30 a.m.

Combined Rates

In 1 hour, the inlet pipe fills 1/10 or 2/20 of the tank, and the outlet pipe empties 1/20 of the tank. The net filling rate is:

Net filling rate 1/10 - 1/20 1/20 of the tank per hour.

Therefore, the tank will get filled in 20 hours, i.e., 2:30 a.m. the next day.

Conclusion

No matter which method you choose, the tank will be completely filled at 2:30 a.m. the next day when both the inlet pipe and outlet pipe are open simultaneously.