Multiple choice general knowledge math & puzzles

The drive from Oakland to Pinewood was a tricky one. I covered the uphill distance of 55 miles at 28 miles per hour. The return journey from Pinewood to Oakland was downhill, and I managed to drive at 70 miles per hour. What was my average speed for the entire journey?

  1. 49

  2. 40

  3. 47

  4. 38
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Average speed is NOT the arithmetic mean of speeds - it's total distance divided by total time. Distance = 55 miles each way = 110 miles total. Time uphill = 55/28 hours, time downhill = 55/70 hours. Total time = 55(1/28 + 1/70) = 55(98/1960) = 5390/1960 hours. Average speed = 110 / (5390/1960) = 110 × 1960/5390 = 40 mph. The arithmetic mean (49 mph) would be wrong because you spend more time at the slower speed.

AI explanation

Because the uphill and return-downhill distances are equal (55 miles each), the correct average speed is the harmonic mean of the two speeds, not the simple arithmetic mean. Harmonic mean = 2 x 28 x 70 / (28+70) = 3920/98 = 40 mph. Using the simple average (49 mph) is the common mistake, since equal-distance trips must be weighted by time spent at each speed, and more time is spent at the slower uphill speed.

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