When skipping rope, the midpoint of the rope can be considered to move on the same circumference. If Xiaoguang uses 0.5 seconds to jump a "single skip" and 0.6 seconds to jump a "double skip", what is the ratio of the speed of the midpoint of the rope when jumping a "single skip" to the speed of the midpoint of the rope when jumping a "double skip"?
(Explanation: "single skip" is one jump where the rope makes one revolution; "double skip" is one jump where the rope makes two revolutions.)
2. Answer: 3: 5

Analysis: Let the radius of the circle traced by the midpoint of the rope be $r$, then the distance the midpoint of the rope travels in one rotation is $2 \pi \mathrm{r}$. The speeds during “single skip” and “double skip” are $\frac{2 \pi_{\mathrm{r}}}{0.5}$ and $\frac{4 \pi_{\mathrm{r}}}{0.6}$, respectively. Therefore, the ratio of the speeds is
$$
\frac{2 \pi_{\mathrm{r}}}{0.5}: \frac{4 \pi_{\mathrm{r}}}{0.6}=\frac{1}{0.5}: \frac{2}{0.6}=\frac{1}{5}: \frac{2}{6}=3: 5
$$