statistics

Let distance between A and B is 'X'  kms

so,  time taken to travel from A to B = 'x' / 500 ( Time = distance / speed)

similarly,  time taken to travel from B to A = 'x' / 700 ( Time = distance / speed)

so  total distance traveled= x + x = 2x

therefore,  speed = distance / time  =  2x / [ x /500 + x /700]  = 2 / [1/500+ 1/700] = 583.33 kms 

Let us assume the distance from A to B to be 3500 Kms. (L.C.M. of 500 & 700)

SPEED                 DISTANCE                TIME

500 Km / Hr.            3500 Kms.               7 Hrs.

700 Km/Hr.               3500 Kms.               5 Hrs.

    Total                      7000 Kms.               12 Hrs.

Average Speed  =  Total Distance  /  Total Time  =  7000  Kms  /  12  Hrs.   =  583.33  Kms. / Hr.