Shnol D.e.

Dima lives in a nine-story building. He descends from his floor to the first floor by elevator in 1 minute. Due to his small height, Dima cannot reach the button for his floor. Therefore, when going up, he presses the button he can reach, and then walks the rest of the way. The entire journey upwards takes 1 minute 10 seconds. The elevator moves up and down at the same speed, and Dima climbs at half the speed of the elevator. On which floor does Dima live?
Let's consider the part of the journey where Dima goes down by elevator and walks up. On the one hand, the walking part takes twice as long, and on the other hand, it is 10 seconds longer. Therefore, the elevator covers this part of the journey in 10 seconds, while Dima takes 20 seconds to walk it. Since the entire elevator ride takes 60 seconds, Dima walks $1 / 6$ of the distance. During this time, he climbs a whole number of intervals between floors. The building is nine-story, so this is one interval, and Dima rides the elevator for 5 intervals. Therefore, he lives on the seventh floor.

## Answer

On the seventh floor.