## Task 2 - 150712

Two vessels, called $A$ and $B$, together have a capacity of exactly 8 liters. A certain amount of water $W$ is distributed between the two vessels such that $A$ is half full and $B$ is completely full. If water is poured from $B$ into $A$ until $A$ is completely full, then $B$ is still one-sixth full. The questions are:

a) the capacity of each of the vessels $A$ and $B$, b) the amount of water $W$.

Determine all the answers to a) and b) that satisfy the given conditions!
(I) If the mentioned properties are present, then it follows:

a) If vessel $A$ has a capacity of $x$ liters, then $B$ has a capacity of $(8-x)$ liters. For this, we have

$$
\frac{x}{2}+8-x=x+\frac{8-x}{6} \quad \Rightarrow \quad x=5
$$

Therefore, only the statement that vessel $A$ has a capacity of 5 liters and vessel $B$ therefore has a capacity of 3 liters can meet the conditions of the problem. Further, it follows:

b) Since $3.0 \mathrm{l} + 2.5 \mathrm{l} = 5.5 \mathrm{l}$, the amount of water $W = 5.5 \mathrm{l}$. Therefore, only this statement can satisfy the requirements.