## 4. Math Puzzle $9 / 65$

A car, whose wheels have a diameter of $\mathrm{d}=56 \mathrm{~cm}$, is supposed to travel at a speed of $v=72 \frac{\mathrm{km}}{\mathrm{h}}$ with an engine speed of $n=3000 \frac{\mathrm{U}}{\min }$.

What gear ratio must the transmission have? (Use $\pi=\frac{22}{7}!$ )
$72 \frac{\mathrm{km}}{\mathrm{h}}=1200 \frac{\mathrm{m}}{\mathrm{min}}, U=\pi d=\frac{56 \cdot 22}{7}=176 \mathrm{~cm}$, The circumference of the wheel is $1,76 \mathrm{~m}$.

For a transmission ratio of $1: 1$, the speed would be $v_{1}=\frac{3000 \cdot 1,76 \mathrm{~m}}{\min }=5280 \frac{\mathrm{m}}{\mathrm{min}}$, but the actual speed $v$ is $1200 \frac{\mathrm{m}}{\mathrm{min}}$. The transmission ratio is

$$
U=\frac{v}{v_{1}}=\frac{1200}{5280}=\frac{5}{22}=1: 4.4
$$