From Zlatoust to Miass, a "GAZ", a "MAZ", and a "KamAZ" set off simultaneously. The "KamAZ", upon reaching Miass, immediately turned back and met the "MAZ" 18 km from Miass, and the "GAZ" - 25 km from Miass. The "MAZ", upon reaching Miass, also immediately turned back and met the "GAZ" 8 km from Miass. What is the distance from Zlatoust to Miass?
Let the distance between the cities be $x$ km, and the speeds of the trucks: "GAZ" - $g$ km/h, "MAZ" - $m$ km/h, "KAMAZ" - $k$ km/h. For each pair of vehicles, we equate their travel time until they meet. We get

$\frac{x+18}{k}=\frac{x-18}{m}, \frac{x+25}{k}=\frac{x-25}{g}$ and $\frac{x+8}{m}=\frac{x-8}{g}$. From this, $\frac{x+18}{x-18} \cdot \frac{x-25}{x+25} \cdot \frac{x+8}{x-8}=\frac{k}{m} \cdot \frac{g}{k} \cdot \frac{m}{g}=1$.

Transform the obtained equation $x^{3}+x^{2}+(18 \cdot 8-18 \cdot 25-8 \cdot 25) x-18 \cdot 8 \cdot 25=x^{3}-x^{2}+(18 \cdot 8-18 \cdot 25-8 \cdot 25) x+$ $18 \cdot 8 \cdot 25 \Leftrightarrow 2 x^{2}=2 \cdot 18 \cdot 8 \cdot 25$. Since

$x>0$, then $x=60$.

## Answer

60 km.