Fix the mistake: Average Speed and Applications of Travel Problems

Average Speed and Advanced Traveler Problems ① Average Speed Going and Returning

When the speeds going and returning are different, the “average speed” is not simply the sum divided by 2. This is a very important point.

🔑 How to Find Average Speed
Average speed = total distance ÷ total time
If the one-way distance is d, the speed going is v₁, and the speed returning is v₂,
Average speed = 2d ÷ (d/v₁ + d/v₂) = 2 × v₁ × v₂ ÷ (v₁ + v₂)
Example: We made a round trip at 40 km/h going and 60 km/h returning. What was the average speed?

Solution:
① Let the one-way distance be 120 km (the least common multiple of 40 and 60).
② Time going → 120 ÷ 40 = 3 hours
③ Time returning → 120 ÷ 60 = 2 hours
④ Total distance 240 km ÷ total time 5 hours = 48 km/h

※ Calculating (40 + 60) ÷ 2 = 50 gives an incorrect answer.

The reason simply adding the speeds and dividing by 2 does not work is that the slower speed takes more time. Always calculate “total distance ÷ total time.”

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