# TIaO - Part 4

**Number Theory**Level 3

Jeremy can control the flow of water in the inlets of a specific tank. The tank has \(2\) inlets. The first inlet can fill the tank in \(4\) hours. The second inlet can fill the tank in \(12\) hours.

He controlled the flow by the following steps:

- First, he made the first inlet flow.
- When the tank was filled by \(\frac{1}{4}\) by the first inlet, he turned off the first inlet and turned on the second inlet.
- When the tank was filled by \(\frac{1}{4}\) by the second inlet, he turned off the second inlet and simultaneously turned both inlets on.
- Finally, when the tank was full, he closed both inlets.

From the time he made the first inlet flow, how many hours did it take him to fill the tank?