A man goes uphill with an average speed of 24 km/h and comes down with an average speed of 36 km/h. The distance travelled in both cases being the same. The average speed for the entire journey is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 28.8 km/h
Average speed is total distance ÷ total time, not the average of the two speeds: the slower part of the trip takes longer and so counts for more.
Assuming each way to be 72 km (a multiple of 24 and 36):
Time uphill \(=\displaystyle\frac{72}{24}=3\) h
Time downhill \(=\displaystyle\frac{72}{36}=2\) h
Average speed \(=\displaystyle\frac{72+72}{3+2}=\frac{144}{5}=28.8\) km/h
Shortcut:
For equal distances at speeds \(a\) and \(b\), average speed \(=\displaystyle\frac{2ab}{a+b}=\frac{2\times24\times36}{60}=28.8\) km/h.