Minimize absolute difference between shortest paths
<p>I am trying to solve the following shortest path problem:</p>

<blockquote>
  <p>There are 2 friends travelling to a city C from cities A and B (one starts at A, the other at B). Find
  the shortest paths that these 2 friends could take from A to C and B to
  C that minimizes the absolute difference between the distance of the 2
  shortest paths.</p>
</blockquote>

<p>I am thinking that using computing shortest paths from A to C and B to C and taking their difference might just work. I do not know whether my solution is correct or how to prove it. Could anyone give me some advice?</p>