A bus travels the first 150 km at 75 km/h and the next 150 km at 50 km/h. What is the average speed for the whole trip?

Question: A bus travels the first 150 km at 75 km/h and the next 150 km at 50 km/h. What is the average speed for the whole trip?

Solution:
Total distance = 150 km + 150 km = 300 km

Now,
Time for first part,
Time = 150/75 = 2 hours

And time for second part,
time = 150/50 = 3 hours

∴ Total time = 2 + 3 = 5 hours

Average speed = Total distance/Total time
= 300/5
= 60 km/h

So the average speed for the whole trip is 60 km/h.

Shortcut:
When equal distances are covered at speeds a and b,
Average speed = 2ab/(a + b)
= (2 × 75 × 50)/(75 + 50)
= 60 km/h