On a railway line, a passenger train departs from location $A$ to location $C$. When the train passes through $B$, a freight train departs from $B$ towards $A$. When the freight train arrives at $A$, a fast train departs from $A$ towards $C$, and this train catches up with the previously mentioned passenger train exactly at the $C$ station. Halfway between $A$ and $B$, a student observes that 15 minutes after the passenger train passes, the freight train passes, and 11 minutes after that, the fast train passes. $B$ is 10 km from $A$. The question is, how many kilometers is $C$ from $B$? (We assume that the trains travel at a constant speed.)