Average Speed

Average speed is never the plain average of two speeds — it is total distance divided by total time. The classic CAT trap: a car goes at 40 km/h one way and 60 km/h back; the average is NOT 50. Because the distance each way is equal, use the harmonic shortcut 2xy/(x + y) = 2·40·60/100 = 48 km/h. The simple mean over-counts the faster leg, which actually takes less time. When the legs cover equal distances at speeds x and y, always use 2xy/(x + y); for three equal legs use 3xyz/(xy + yz + zx). The simple average (x + y)/2 applies only when equal TIMES are spent at each speed — a distinction CAT exploits constantly. When in doubt, assume a convenient distance (the LCM of the speeds works beautifully) and compute total distance over total time directly.

✅ Solved examples

✏️ Practice — try these, take hints as needed

📝 Topic test — 8 questions

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