GMAT Focus EditionQuantitative ReasoningHard
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 90 km/h. What is the average speed for the entire round trip?
- A80 km/h
- B70 km/h
- C72 km/h
- D75 km/h
Show answer & explanationAnswer & explanation
Correct answer: C. 72 km/h
Let the distance between City A and City B be 'D'. Time taken to travel from A to B (t1) = D/60. Time taken to travel from B to A (t2) = D/90. Total distance = D + D = 2D. Total time = t1 + t2 = D/60 + D/90 = (3D + 2D)/180 = 5D/180 = D/36. Average Speed = Total Distance / Total Time = 2D / (D/36) = 2D * (36/D) = 72 km/h. This is a harmonic mean of the two speeds.
Why the other options are wrong
- A. This is incorrect; it might be a result of miscalculation or an incorrect average.
- B. This is incorrect; it might be a result of miscalculation or an incorrect average.
- D. This is incorrect; it is the simple arithmetic mean of the two speeds, which is incorrect for average speed over different times.
Average Speed (Round Trip)
The total distance traveled divided by the total time taken for a journey that involves traveling the same distance at different speeds.
- It is NOT the arithmetic mean of the speeds.
- It is the harmonic mean of the speeds: 2 / (1/v1 + 1/v2).
- To calculate, assume a distance or use the formula for harmonic mean.
Memory trick: Distance over time, for each leg, then total distance over total time to beg.