Ya. I. V.

From the volcano station to the summit of Stromboli volcano, it takes 4 hours to walk along the road, and then - 4 hours along the path. At the summit, there are two craters. The first crater erupts for 1 hour, then remains silent for 17 hours, then erupts again for 1 hour, and so on. The second crater erupts for 1 hour, remains silent for 9 hours, erupts again for 1 hour, and so on. During the eruption of the first crater, it is dangerous to walk both along the path and the road, while during the eruption of the second crater, only the path is dangerous. Vanya saw that at exactly 12 o'clock, both craters started erupting simultaneously. Will he ever be able to climb to the summit of the volcano and return, without risking his life?
The path along the road and the trail (there and back) takes 16 hours. Therefore, if you start immediately after the eruption of the first crater, this crater will not be dangerous.

Movement along the trail (there and back) takes 8 hours. Therefore, if you start moving along the trail immediately after the eruption of the second crater, this crater will not be dangerous.

For Vanya to have a safe ascent, it is sufficient for the first crater to stop erupting by the start of movement along the road, and for the second crater to stop erupting 4 hours later, by the start of movement along the trail.

![](https://cdn.mathpix.com/cropped/2024_05_06_dc53e83c4670b2e19022g-10.jpg?height=57&width=1995&top_left_y=2375&top_left_x=40)
11th, 21st, 31st, 41st hours. Therefore, if you start at the beginning of the 38th hour, Vanya will reach the start of the trail just as the second crater finishes erupting, as required.