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.