The radius of the rear wheel of a car is twice as large as that of the front wheel. If the circumference of the front wheel were 5 dm larger, and that of the rear wheel 5 dm smaller, then the front wheel would make the same number of revolutions over $150 \mathrm{~m}$ as the rear wheel over $187.5 \mathrm{~m}$. What is the radius of the two wheels?
Let the radii (measured in dm) be $x$ and $2x$. To use the data from the second sentence, the number of revolutions is given by the ratio of the distance traveled to the circumference, naturally both measured in the same length unit (here, the distance is also measured in dm). Therefore,

$$
\frac{1500}{2 \pi x + 5} = \frac{1875}{4 \pi x - 5}
$$

and from this,

$$
x = \frac{16875}{2250 \pi} = \frac{15}{2 \pi} \approx 2.39
$$

Accordingly, the radii of the wheels are 2.39 and 4.78 dm, and their diameters (which are often more important, easier to measure, or better usable in practical life) are 4.78 and $9.56 \, \text{dm}$.

Eva Simon (Szombathely, Kanizsa Dorottya Secondary School I. o. t.)

Note. Many solvers, in good faith, calculated the radii with 5-6 decimal places of "precision." This is unnecessary for two reasons: 1. Even by writing two decimal places, we get the result rounded to millimeters, which is a satisfactory precision in practice; 2. The value $\pi \approx 3.14$ is also a result of rounding, with "significant digits" of three, so it is not possible to calculate more than three reliably accurate digits in the ratio formed with it.