# Task № 2

The captain's assistant, observing the loading of the ship, smoked one pipe after another from the start of the loading. When $2 / 3$ of the number of loaded containers became equal to $4/9$ of the number of unloaded containers, and the ship's bells struck noon, the old seafarer began to light another pipe. When he finished smoking it, the ratio of the number of loaded containers to the number of unloaded containers became the inverse of the ratio that existed before he started smoking that pipe. How many pipes did the second assistant smoke during the loading (assuming that the loading speed, as well as the smoking speed, remained constant throughout the process.)
Answer: The assistant smoked 5 pipes.

## Solution.

Let $x$ be the part of containers that were loaded by noon, and $y$ be the remaining part of containers. Then from the conditions we get: $\left\{\begin{array}{l}\frac{2}{3} x=\frac{4}{9} y \\ x+y=1\end{array} \Rightarrow x=\frac{2}{5}, \quad y=\frac{3}{5}\right.$.

After smoking one pipe, the ratio became reversed, meaning the part of loaded containers became equal to $3 / 5$, and thus, during this time, they loaded $1 / 5$ of the containers. Therefore, the captain's assistant smoked 5 pipes during the loading.