# Tank Filling Riddle

A large water tank has two inlet pipes (a large one and a small one) and one outlet pipe. It takes 3 hours to fill the tank with the large inlet pipe. On the other hand, it takes 6 hours to fill the tank with the small inlet pipe. The outlet pipe allows the full tank to be emptied in 9 hours.

What fraction of the tank (initially empty) will be filled in 0.64 hours if all three pipes are in operation? Give your answer to two decimal places (e.g., 0.25, 0.5, or 0.75).

**0.25**

The large inlet can fill the tank in 3 hrs., which means that, in 1 hr., it can fill 1/3 of the tank. Similarly, the smaller inlet takes 6 hrs. to fill the tank, which means it can fill 1/6 of the tank in one Hr. Thus, if both inlets are opened at the same time, it will fill 1/3 + 1/6 = **1/2 **of the tank **in 1 hr. **However, the outlet will empty the tank in 9 hrs., which means that, in 1 hr., it will empty **1/9** of the tank. Thus, if all 3 pipes are opened simultaneously, the net effect in one hr. will be that (**1/2 – 1/9**) of the tank will be filled.

Hence, the portion of the tank that will be filled in in 0.64 hrs. will be **(1/2- 1/9) * 0.64** = 0.2488… ~ **0.25**

### Your Answer

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