A particle covers half of its total distance with speed v1 and the rest half distance with speed v2. Its average speed during the complete journey is?

Let the total distance be S.
The particle covers S/2 with speed v1 and S/2 with speed v2.
Time taken to cover the first half distance t1 = S/(2v1)
Time taken to cover the second half distance t2 = S/(2v2)
Total time taken t = t1 + t2 = S/(2v1) + S/(2v2) = S(v1 + v2)/(2v1v2)
Average speed Vav = Total distance / Total time = S / [S(v1 + v2)/(2v1v2)] = 2v1v2/(v1 + v2)