I'm missing a factor of 1/2


d = (1/2)at^2


since v = at and d = integral[(at)dt]


so the final equation is:


avg. speed =


2sqrt(2d)sqrt(a1a2)/[sqrt(a1)+sqrt(a2)]


My example of 6 mph/sec and 4 mph/sec for a mile gives an average speed of 187 mph.