## 5. Soba

Ana can paint the room in 15 hours, Barbara in 10 hours, and Cvijeta twice as fast as Ana. Ana starts painting and paints alone for one and a half hours, then Barbara joins her and they paint together until half the room is painted. After that, Cvijeta joins them and all three paint until the entire room is painted. How many minutes in total did it take to paint the room?

Result: $\quad 334$
## Solution.

Ana paints $\frac{1}{15}$ of the room in 60 minutes, and in 90 minutes she paints $1.5 \cdot \frac{1}{15}=\frac{1}{10}$ of the room.

Ana and Barbara together need to paint $\frac{4}{10}$ of the room. Together, they paint $\frac{1}{15}+\frac{1}{10}=\frac{1}{6}$ of the room in 60 minutes, so they will paint $\frac{4}{10}$ of the room in $\frac{4}{10}: \frac{1}{6}=\frac{12}{5}$ hours, or 144 minutes.

Ana, Barbara, and Cvijeta together need to paint half of the room. Together, they paint $\frac{1}{15}+\frac{1}{10}+\frac{2}{15}=\frac{3}{10}$ of the room in 60 minutes, so they will paint $\frac{1}{2}$ of the room in $\frac{1}{2}: \frac{3}{10}=\frac{5}{3}$ hours, or 100 minutes.

The entire room is painted in $90+144+100=334$ minutes.