My canal boat tour

Have you ever been in Amsterdam? Next time take a canal boat tour. I had the great opportunity to do it. When the Capitan of the boat had to make a 90 degree turn from one narrow canal to another one a little bit wider, he used much skills, and a lot of maneuvering to pass through. At that moment I asked myself some questions. I want to share with you one of them. A wooden pole with a negligible width floats down a canal, p foot wide and approaches the T-intersection with a canal, q foot wide. Find the pole with maximum length m , that will turn the corner and pass through the intersection.