On a journey of 300 km, a person travels the first 100 km at the speed of 40 km/hour, the next 50 km at the speed of 60 km/hour and the last 150 km at the speed of 50 km/hour. What is his average speed (in km/hour) for the entire journey?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 47.36
Average speed is the total distance divided by the total time. The time for each part is its distance divided by its speed.
Time for each part:
First 100 km at 40 km/h: \(\displaystyle\frac{100}{40}=2.5\) h
Next 50 km at 60 km/h: \(\displaystyle\frac{50}{60}=\frac{5}{6}\) h
Last 150 km at 50 km/h: \(\displaystyle\frac{150}{50}=3\) h
Average speed:
Total time \(\displaystyle =2.5+\frac{5}{6}+3=\frac{19}{3}\) h
Average speed \(\displaystyle =300\div\frac{19}{3}=\frac{900}{19}=47.36\ldots\) km/h
Tip: The plain average of the three speeds, \((40+60+50)\div3=50\), is wrong because the person spends different times at each speed; always divide total distance by total time.