B3. Tanks $A$ and $B$, which are of cylindrical shape, have a volume of $1000 \ell$. Tank $A$ contains $500 \ell$, and tank $B$ contains $200 \ell$ of water. Water is transferred from tank $A$ to tank $B$ through a pipe. Every minute, $5.5 \ell$ of water flows through.

(a) How much water is in tank $A$ after 10 minutes?

(b) After how long would tank $B$ contain $530 \ell$ of water?

(c) Calculate after how long the amount of water in both tanks will be equal. Round the result to the nearest minute.

(d) To what height is tank $A$ filled at the start of the transfer if its diameter is $60 \mathrm{~cm}$? Round the result to two decimal places.

## 22nd Mathematics Knowledge Competition for Vocational School Students  National Competition, April 23, 2022

## Solutions to the Problems for 1st and 2nd Year Students

| $\mathrm{A} 1$ | $\mathrm{~A} 2$ | $\mathrm{~A} 3$ | $\mathrm{~A} 4$ | $\mathrm{~A} 5$ | $\mathrm{~A} 6$ | $\mathrm{~A} 7$ | $\mathrm{~A} 8$ | $\mathrm{~A} 9$ | $\mathrm{~A} 10$ |
| :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: |
| B | $\mathrm{D}$ | $\mathrm{B}$ | $\mathrm{C}$ | $\mathrm{B}$ | $\mathrm{B}$ | $\mathrm{D}$ | $\mathrm{D}$ | $\mathrm{B}$ | $\mathrm{A}$ |
B3.

(a) In tank $A$, after ten minutes, the amount of water is $500-55=445 \ell$.

(b) We write the equation $200+5.5 x=530$. The solution is $x=60$. In tank $B$, there would be $530 \ell$ of water after 60 minutes or 1 hour.

(c) If we write the equation, $500-5.5 x=200+5.5 x$, we get the solution $x=27.3$. In both tanks, the amount of water would be the same after 27 minutes.

(d) The desired height is calculated using the formula $v=\frac{V}{\pi r^{2}}=\frac{500 \mathrm{dm}^{3}}{\pi(3 \mathrm{dm})^{2}}=17.68 \mathrm{dm}$.

(a) The calculated amount of water is $445 \ell$.

(b) The calculated filling time for tank B is 60 min.

(c) The calculated time when the amount of water in both tanks will be the same is 27 min. $.2 \mathrm{t}$

(d) The calculated height of the water in tank A is $17.68 \mathrm{dm}$.