A drive took some hours to travel from Rome to Milan. His average speed for the whole journey was 80 km/hour. For the first half of the journey he traveled at an average speed of 50km/hour.

Question

Find his average speed for the second half of the journey. In this case half refers to half of the time.
Find his average speed for the second half of the journey. In this case half refers to half of the distance.

Answer 1

Let half the journey, time wise, be x hours.
Thus the full journey time is 2x hours.
Avg speed = total distance/total time
80 = total distance/2x
Thus total distance=160x km
For the first part of the journey, his distance travelled was speed x time, or 50x km
For the second part of the journey, his distance travelled was160x - 50x = 110x km.
Thus his average speed in the second part of the journey was distance/ time = 110x/x = 110 km/hr.
Use a similar strategy for part 2 of your question.