Propositiones ad Acuendos Juvenes/Problems/8 - De Cupa

by : Problem $8$

 * De Cupa: A Cask and Three Pipes
 * A cask is filled with $100$ metretae through $3$ pipes.
 * One third plus one sixth of the capacity flows through one pipe,
 * one third of the capacity flows through another,
 * but only a sixth of the capacity flows through the third.


 * How many sextarii flow in through each pipe?

Solution

 * $3600$ sextarii flow in through the first pipe;
 * $2400$ sextarii flow in through the second pipe;
 * $1200$ sextarii flow in through the third pipe.

Proof
First note that there are $72$ sextarii to the metreta.

Hence there are $7200$ sextarii in total in the cask.

Through the first pipe we have:
 * $\dfrac 1 3 \times 7200 + \dfrac 1 6 \times 7200 = 3600$

Through the second pipe we have:
 * $\dfrac 1 3 \times 7200 = 2400$

Through the third pipe we have:
 * $\dfrac 1 6 \times 7200 = 1200$