## 205. Math Puzzle $6 / 82$

A machine with a base length of $1.20 \mathrm{~m}$ is to be rolled forward using some rollers, each with a diameter of $10 \mathrm{~cm}$.

How far can the machine be moved before the roller placed at the back of the machine re-emerges?
When advancing, the rollers under the machine cover the same distances relative to the floor and the machine frame.

If the machine is pushed forward by $s$ meters, the rollers only roll forward by $\frac{s}{2}$ meters. And the frame rolls forward by $\frac{s}{2}$ meters relative to the rollers.

If in our example the machine moves forward by 2.40 meters, the roller covers 1.20 meters relative to the machine base. It reappears by another 1.20 meters.