B3. Tanks $A$ and $B$, which have the same 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 will tank $B$ contain $530 \ell$ of water?

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

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

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

## Problems for 3rd Year

Time for solving: 90 minutes. In section A, we will award two points for a correct answer and deduct half a point for an incorrect answer. Enter the answers for section A in the left table. In section B, we will award up to seven points for a correct answer.

| A1 | A2 | A3 | A4 | A5 | A6 | A7 | A8 | A9 | A10 |
| :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- |
|  |  |  |  |  |  |  |  |  |  |

![](https://cdn.mathpix.com/cropped/2024_06_07_a04162d2cc6b04e5d61eg-06.jpg?height=160&width=320&top_left_y=565&top_left_x=1416)
B3.

(a) The volume of water in tank $A$ after ten minutes is $500-55=445 \ell$ of water.

(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 same amount of water would be present 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 volume of water $445 \ell$. ........................................................................................

(b) The calculated filling time for tank B 60 min. ..................................................... 2 t

(c) The calculated time when the amount of water in both tanks will be the same 27 min. ........................ 2 t

(d) The calculated height of water in tank A 17.68 dm. ................................................... 2 t

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

## Solutions to Problems for 3rd Year

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