1. A bridge over a river connects two different regions of the country. Once, one of the regions repainted the part of the bridge that belonged to it. If the freshly painted part of the bridge were 1.2 times larger, it would make up exactly half of the entire bridge. What part of the bridge needs to be repainted to make it exactly half painted?
# Solution

Let $x$ be the painted part of the bridge. (We take the entire bridge as one unit.) According to the condition,

$$
1.2 x = 1 / 2 \Longrightarrow x = \frac{5}{12}
$$

To complete the painting, we need

$$
\frac{1}{2} - \frac{5}{12} = \frac{1}{12}
$$

Answer: $\frac{1}{12}$ part.