Daily Math Puzzle: 2026-06-20
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2026-06-20
The Great Mysterio performs his famous 'Temporal Travel' illusion. He announces that he will travel from one end of his grand stage to the other and immediately return. Spectators with enchanted stopwatches observe that he makes the journey *to* the far end of the stage at an apparent speed of 60 km/h. For the return journey, his speed seems to slow to 40 km/h. Mysterio then challenges the audience: 'What was my average speed for the *entire* round trip, from start to finish?'
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Solution
48 km/h — Many people are tempted to simply average the two speeds (60 km/h + 40 km/h) / 2 = 50 km/h. However, this is incorrect because average speed is defined as Total Distance / Total Time, not the average of speeds. Since Mysterio spends more time traveling at the slower speed, it pulls the overall average down.
Let 'D' be the distance from one end of the stage to the other.
Total Distance = D (to the far end) + D (back to start) = 2D.
Time taken to travel to the far end (t1) = Distance / Speed = D / 60 hours.
Time taken for the return journey (t2) = Distance / Speed = D / 40 hours.
Total Time = t1 + t2 = (D / 60) + (D / 40)
To add these fractions, find a common denominator, which is 120:
Total Time = (2D / 120) + (3D / 120) = 5D / 120 = D / 24 hours.
Now, calculate the Average Speed = Total Distance / Total Time
Average Speed = 2D / (D / 24)
Average Speed = 2D * (24 / D)
Average Speed = 48 km/h.
The length of the stage (D) cancels out, so its specific value is not needed to find the average speed.
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