George Strain and I played some doubles Joust recently. In the first game the ratio of George's score to mine was P to 1. In the second game, coincidentally, we played to the same total score, and the ratio of his score to mine was Q to 1.
What was the ratio of his combined score to mine for the two games?
Please PM your answers rather than post to this thread so that I may have a winner in each of two forums. If you give an incorrect answer, please excuse yourself from further guessing on that forum. (You may try one answer in each forum if you are a member of both.)
To keep things moving along, I will post any incorrect answers given, but won't tell who gave them.
For the first correct answer on each forum, I have the usual Golden Era Game of the Week t-shirt:


If you already have one, you're just playing for fun.
The problem is not terribly difficult, but may be slightly more complicated than it would appear at first glance.