GMAT Focus EditionQuantitative ReasoningMedium
A car travels from City A to City B at an average speed of 60 km/h and returns from City B to City A at an average speed of 40 km/h. What is the average speed for the entire round trip?
- A50 km/h
- B55 km/h
- C52 km/h
- D48 km/h
Show answer & explanationAnswer & explanation
Correct answer: D. 48 km/h
Average speed is Total Distance / Total Time. Let the distance between City A and City B be D. Time to A to B = D/60. Time to B to A = D/40. Total Distance = D + D = 2D. Total Time = D/60 + D/40 = (2D + 3D)/120 = 5D/120 = D/24. Average Speed = 2D / (D/24) = 2D * (24/D) = 48 km/h. This is also a harmonic mean: 2 / (1/60 + 1/40).
Why the other options are wrong
- A. Incorrect. This is the simple arithmetic average (60+40)/2 = 50, which is incorrect for average speed over different times.
- B. Incorrect. This is a common distractor based on miscalculation.
- C. Incorrect. This is a common distractor based on miscalculation.
Average Speed (Round Trip)
For a round trip with different speeds, the average speed is calculated as total distance divided by total time, which is equivalent to the harmonic mean of the two speeds.
- Not the simple arithmetic average of speeds.
- Harmonic mean formula: 2 / (1/v1 + 1/v2).
- Requires considering time spent at each speed.
Memory trick: Distance over time, that's speed's true rhyme; average speed, total path, total time.