Notorious Tank Problem

The notorious Tank Problem that one finds in every single collection of arithmetical and algebraic problems. No doubt, you all remember those classic scholastically dry problems of this order:

"The tank has two pipes -- one leading to fill the tank to the brim and the other out. the first needs five hours to fill the tank and the second ten hours to drain it dry. How long will it take the tank to fill up when the stop cocks are out of both pipes ?"




This problem has a venerable history, dating right back some twenty centuries to Heron of Alexandria. Here is one from his collection for your free time in the weekend.

Four Fountains are there and a reservoir vast.
In but one day the first doth fill it to the brim.
The second two days and nights must play to do the same.

The third takes thrice the time as did the first.
The fourth comes last with four days and nights.
Now tell me when the reservoir will fill,
when all four play at once.



It is two thousand years now that the tank problem has posed and -- such is the force of habit ! -- has been solved wrongly in all this time.