Aman goes uphill with an average speed of 30 km/h and comes down with an average speed of 40 km/h. The distance travelled in both cases is the same. The average speed for the entire journey is ________.
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 34.28 km/h
Average speed is total distance divided by total time. The slower part of the trip takes longer, so for equal distances the average lies below the simple average of the two speeds.
Assuming each way to be 120 km:
Time uphill \(=\displaystyle\frac{120}{30}=4\) h, time downhill \(=\displaystyle\frac{120}{40}=3\) h
Average speed \(=\displaystyle\frac{240}{7}\approx34.28\) km/h
Tip: For two equal distances at speeds x and y, the average speed is \(\displaystyle\frac{2xy}{x+y}=\frac{2\times30\times40}{70}\), never the plain average \(\frac{30+40}{2}=35\).