a vehicle travels half the distance l with speed v1 and half with speed v2. its average speed is
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v1=L/2/t1,v2=L/2/t2
L=2v1t1,L=2v2t2
t1=L/2v1,t2=L/2v2
Vavg=total distance/total time=L/(L/2v1+L/2v2)
Vavg=(L/L/2)*1/(1/v1+1/v2)=2v1v2/v1+v2
Vavg=(2v1v2)/(v1+v2)
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