My solution to this problem is (1) avoid instant messaging at all costs, and (2) delay responding to any mail that is either (a) a contextless plea for handholding ("I have a problem, do you have some time?"), or (b) best solved by the asker taking some time to educate themselves.

It's a win-win, because either the asker learns they can solve their problems more quickly by Googling it themselves, or I can limit my responses to a rate that is below my daily (or weekly) annoyance threshold.