Matrices & Systems · Medium problem

A delivery service maps the distances (in miles) between three depots, $1$, $2$, and $3$. The distance between depots $1$ and $2$ is a fixed $15$ miles. A field survey recorded the other two distances from BOTH directions: $d_{13}=3a-2$ and $d_{31}=a+8$, and $d_{23}=5b-1$ and $d_{32}=2b+11$. Since distance is symmetric, $d_{13}=d_{31}$ and $d_{23}=d_{32}$. A truck must visit all three depots and return to its start. Find the total length of this round trip.