Average speed of a round trip — Aptitude Question
Average speed of a round trip: A car travels from P to Q at 60 km/h and returns at 40 km/h. Answer and worked solution on CodeKairo.
- Topic: Time, Speed & Distance
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 50 seconds
Question
A car travels from P to Q at 60 km/h and returns at 40 km/h. What is the average speed for the whole trip?
Options
- 45 km/h
- 48 km/h
- 50 km/h
- 52 km/h
Show the answer and the worked solution
Correct answer: B. 48 km/h
Worked solution
- Let PQ = 120 km (any distance works). Going: 120/60 = 2 h. Returning: 120/40 = 3 h.
- Average = 240 km / 5 h = 48 km/h.
- Or 2 × 60 × 40 / (60 + 40) = 4800/100 = 48.
Answer: 48 km/h.
The idea
Equal distances at speeds a and b average to the harmonic mean 2ab/(a + b), always below the arithmetic mean. Equal times would average to (a + b)/2.
Shortcut. The harmonic mean of two speeds is their product over their plain mean: 2,400 ÷ 50 = 48 km/h.
Common trap. 50 km/h — the plain mean of 60 and 40; the slower return lasts longer (3 h against 2 h for 120 km), dragging the average down to 48.