13.072. The city $C$, located between points $A$ and $B$, is supplied with gas from these points, the distance between which is 500 km. From reservoir $A$, 10000 $\mathrm{M}^{3}$ of gas is pumped out every minute, and from reservoir $B$ - 12% more. In this case, the gas leakage in each pipeline is 4 m $^{3}$ per kilometer of pipe. Knowing that gas arrives in city $C$ from reservoirs $A$ and $B$ equally, find the distance between city $C$ and point $A$.
## Solution.

Let $x$ km be the distance between $A$ and $C$, and $500-x$ km be the distance between $C$ and $B$. Considering the gas leakage, $10000-4 x$ m$^3$ of gas is delivered from $A$ to $C$, and $10000 \cdot 1.12 - 4(500-x)$ m$^3$ of gas is delivered from $B$ to $C$. According to the condition, $10000-4 x = 1.12 \cdot 10000 - 4(500-x)$, from which $x=100$.

Answer: 100 km.