Anna went from home to school with the speed 3 km/hour. she ran back home with the speed 6 km/hour. her sister olga went to school and back with the same speed, and she spent as much time on the road as anna. what was olga's speed?

Let:
v = Olga's speed
t = the time Anna spent going to school (3 km/hour)
t/2 = the time Anna spent running back home with speed of 6 km/hour
So, t + t/2 = 3t/2 is the total time
In the meantime distance = speed*time and the both made the same distance we can put it as:
3t + 6*(t/2) = (3t/2)*v
6t = (3/2)tv divide both sides by t 
(3/2)v = 6
v = 2*6/3
v = 4 km/hour
Olga's speed was 4 km/hour.