## 265. Math Puzzle $6 / 87$

For a motorcycle, the optimal rotational speed of the engine shaft is $6000 \mathrm{U} / \mathrm{min}$.

What is the gear ratio of the rear axle to the engine shaft produced by the transmission if the optimal rotational speed results in a speed of $60 \mathrm{~km} / \mathrm{h}$?

The diameter of the rear wheel is $53 \mathrm{~cm}$ (circumference 1.67 m).
RPM of the rear wheel $=n_{H}, V=n_{H} \cdot d \cdot \pi$

$$
n_{H}=\frac{V}{d \cdot \pi}=\frac{60 \mathrm{~km}}{0.53 \cdot 3.14 \mathrm{~m} \mathrm{~h}}=\frac{1000 \mathrm{~m}}{0.53 \cdot 3.14 \mathrm{~m} \mathrm{~min}}=600 \mathrm{U} / \mathrm{min}
$$

RPM ratio $n_{H}: n_{\text {Motor }}=600: 6000=1: 10$

For the motorcycle, the RPM of the rear wheel to the optimal engine RPM is $1: 10$.