The average method doesn't work for an interesting reason. Because the courier spends much longer catching up with the front of the convoy, he will be travelling at the slower speed (relative to the convoy) for a longer period of time. But when you average the two speeds, you're implicitly giving both legs an equal time-weighting.
E.g.1 I spend 1 hour walking at 2 mph, then I spend 1 hour running at 5 mph. Average speed = (2+5)/2. It is okay to average here because both speeds lasted the same amount of time.
E.g.2 I walk 1 mile at 2 mph, then run 1 mile at 5 mph. Average speed =/= (2+5)/2 ! It is not okay to average - even though the distance travelled is the same, the time spent doing each activity is not. Correct answer, work it out the long way: time spent walking = 0.5 hours; time spend running = 0.2 hours; total time spent = 0.7; average speed = total distance / total time = 2/0.7 = ~= 2.8 mph. Which is less than 3.5 mph (the average of 2 and 5).
Be wary of shortcuts!