Concerned with the 2005 relaunch:
Do we have an estimate for how long the Doctor travels on his own between visits with his companions while he actively "has" companions?
While watching the 11th and 12th Doctor's adventures, it seems as if his companions (Amy and Clara, specifically) were left alone at times to lead a "normal" life between their trips in the TARDIS.
But given the nature of the Doctor and the TARDIS, there's no reason that he would spend the same amount of time away from his companions as his companions spend away from him (from each of their own perspectives).
So, how long is he away?
An average is probably the only reasonable result. I'd think we'd have to take at least 2 mentions of the Doctor's age that we can take as accurate (for the sake of the question), and divide it by the number of known companion adventures. But, this may be more difficult than just getting an episode count, because we see in S8's The Caretaker that Clara is going on very many adventures not chronicled in their own full episodes, each separated by time at home without the Doctor.
This also isn't meant to be a question of "How much has the Doctor aged since the show began", because there are implied large gaps between him having companions, and those should be removed from the equation (such as the time between 10th's regen and 11th's picking of Amy as a companion, or the time between the Pond's and Clara).