Question

On a long journey if 10% of the distance is covered at an average speed of 40 km/h and 90% of the distance is covered at an average speed of 90 km/h. What is the average speed for the entire journey? How does this answer change if the percentages relate to time rather than distance, that is, if 10% of the duration is covered at 40 km/h and 90% of the duration is covered at average speed of 90 km/h.

Answer 1

First case:
Total distance = L (km)
Time at 40 km/h = 0.1 L/40
Time at 90 km/h = 0.9 L/90
Total time = (.0025+.01)L
Average speed = L/(.0125) = 80 km/h

Second case:
Total trip time = T
Distance covered at 40 km/h = 40*0.1T = 4.0 T km
Distance travelled at 90 km/h = 90*0.9T = 81 T km
Average speed = 85T/T = 85 km/h