A railway line is divided into $10$ sections by the stations $A, B, C, D, E, F, G, H, I, J$ and $K$. The distance between $A$ and $K$ is $56$ km. A trip along two successive sections never exceeds $12$ km. A trip along three successive sections is at least $17$ km. What is the distance between $B$ and $G$?
I have no idea how to solve this question. I thought about taking the distance between each set of successive stations as a variable, but this gets too messy. And taking ${56\over10}=5.6$ doesn't work as well. The inequalities look like they're important, but I can not make use of them anywhere.
Please help.