A journey in three equal parts — Aptitude Question
A journey in three equal parts: A man covers equal distances at 10, 20 and 60 km/h. What is his average speed for… Answer and worked solution on CodeKairo.
- Topic: Time, Speed & Distance
- Section: Quantitative Aptitude
- Difficulty: Hard
- Time target: 90 seconds
Question
A man covers equal distances at 10, 20 and 60 km/h. What is his average speed for the whole journey?
Options
- 18 km/h
- 20 km/h
- 24 km/h
- 30 km/h
Show the answer and the worked solution
Correct answer: A. 18 km/h
Worked solution
- Take each stretch as 60 km. Times: 6 h, 3 h and 1 h.
- Total = 180 km in 10 h.
- Average = 18 km/h.
Answer: 18 km/h.
The idea
For equal distances the average is the harmonic mean 3/(1/10 + 1/20 + 1/60). Choosing the LCM of the speeds as the distance makes every time a whole number.
Shortcut. One kilometre of each stretch takes 1/10 + 1/20 + 1/60 = 1/6 h, so 3 km take 1/6 h — 18 km/h.
Common trap. 30 km/h — averaging the three speeds, (10 + 20 + 60) ÷ 3; six of the ten hours are spent at 10 km/h, so the true average is far lower.