A steel rod and a zinc rod are each 2 meters long at $80^{\circ}$ Celsius. At what temperature would they show a difference of $1.5 \mathrm{~mm}$? The linear expansion coefficient of steel is 0.0000118 and that of zinc is 0.000031.
At the sought temperature $x$, the lengths of the iron and zinc rods are

$$
2 \times \frac{1+0.0000118 \times x}{1+0.0000118 \times 80}
$$

and

$$
2 \times \frac{1.000031 \times x}{1.000051 \times 80}
$$

The difference between them is therefore

$$
2 \times \frac{1.0000118 \times x}{1.0000118 \times 80}-2 \times \frac{1.000031 \times x}{1.000031 \times 80}= \pm 0.0015
$$

The expressions under 1) and 2) can be written in the following form with a large approximation (which we can verify by performing the indicated division):

$$
2(1+0.0000118(x-80)) \quad \text { and } \quad 2(1+0.000031(x-80))
$$

Thus, 3) takes the following simple form:

$$
x-80=\frac{ \pm 0.0015}{2 \times 0.0000192}= \pm 39
$$

from which

$$
x_{1}=119^{\circ} \quad \text { and } \quad x_{2}=41^{\circ} \text {. }
$$

(Imre János, fgymn. VIII. o. t. Nyíregyháza.)

The problem was also solved by: Gara Zoltán, fg. VIII. Nyíregyháza; Jankovics György, fg. VIII. Losoncz; Sramkó Loránd, fg. VIII. Rimaszombat; Suták Sándor, fg. VIII. Nyíregyháza.