GMAT Focus EditionQuantitative ReasoningMedium
A car travels from Town X to Town Y at an average speed of 40 mph and returns from Town Y to Town X at an average speed of 60 mph. What is the average speed for the entire round trip?
- A50 mph
- B48 mph
- C55 mph
- D52 mph
Show answer & explanationAnswer & explanation
Correct answer: B. 48 mph
For average speed over a round trip with different speeds but the same distance, use the formula: Average Speed = (2 * S1 * S2) / (S1 + S2). Here, S1 = 40 mph and S2 = 60 mph. So, Average Speed = (2 * 40 * 60) / (40 + 60) = (4800) / (100) = 48 mph.
Why the other options are wrong
- A. This is the simple arithmetic average (40+60)/2, which is incorrect because time spent at each speed is different.
- C. This is a plausible distractor if the formula is misapplied or misremembered.
- D. This could result from a calculation error in the formula.
Average Speed (Round Trip)
The average speed for a journey where the distance traveled in each direction is the same but the speeds are different, calculated using the harmonic mean.
- Average Speed = Total Distance / Total Time.
- For equal distances with two speeds (S1, S2): Average Speed = (2 * S1 * S2) / (S1 + S2).
- The average speed is always closer to the slower speed.
Memory trick: Don't just average the speeds, factor in the time spent!