7. (10 points) Two wheels rotate, meshed with each other, around fixed axes passing through the centers of wheels $A$ and $B$. The radii of the wheels differ by a factor of three. The larger wheel makes 10 revolutions per minute. Determine how many seconds the smaller wheel spends on one revolution?

![](https://cdn.mathpix.com/cropped/2024_05_06_31c3376e8d47665bbf90g-09.jpg?height=406&width=488&top_left_y=962&top_left_x=864)
Answer: $2 c$

Solution. The speeds of points lying on the edge of the wheels are the same.

The distances traveled by these points differ by three times.

The large wheel spends on one revolution

$$
t_{\text {large }}=\frac{1 \text { min }}{10 \text { revolutions }}=\frac{60 \text { s }}{10 \text { revolutions }}=6 \text { s }
$$

Therefore, the small wheel spends on one revolution $t_{\text {small }}=\frac{1}{3} t_{\text {large }}=\frac{6}{3}=2 c$