Suresh covers a distance by a cycle at 10 km/h. He returns to the starting point in a car at a speed of 50 km/h. Find the average speed for the entire journey.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 16.66 km/h
Average speed is total distance divided by total time. The slow trip by cycle takes much longer than the trip back by car, so the average lies much nearer 10 than 50; it is not the plain average of the two speeds.
Assuming the one-way distance to be 50 km:
Time by cycle \(=50\div10=5\) h
Time by car \(=50\div50=1\) h
Average speed \(\displaystyle =\frac{50+50}{5+1}=\frac{100}{6}\approx16.66\) km/h
Shortcut: For the same distance covered at speeds \(a\) and \(b\), the average speed is \(\displaystyle \frac{2ab}{a+b}=\frac{2\times10\times50}{10+50}=\frac{1000}{60}\approx16.66\) km/h.