This is a very interesting topic and one that many researchers have asked. The activation of T cells happens in three steps, and this leads to different timing in the activation process, minutes, hours, and even days.
This paper will be of interest to you as it reviews key findings in each of the activation steps and attempts to answer your question about how many APCs it takes to activate a T cell. Other authors that have studied this area are Mark Davis (Stanford University) and Uli von Andrian (Harvard).