Here is a simple word problem: a vehicle travels 80 km in 2 hr, then 60 km in 1 hr. What is its average speed?

It is ambiguous because the independent variable is not stated or implied. Was the distance measured based on the time, or was the time measured based on the distance? In the former case, time is the independent variable, but in the latter case distance is the independent variable.

Solution 1: if time is the independent variable, the answer is the arithmetic mean: (80/2 + 60/1)/2 = (40 + 60)/2 = 50 km/hr.

Solution 2: if distance is the independent variable, the answer is the harmonic mean: ((2/80 + 1/60)/2)^{−1} = ((2 + 3)/240)^{−1} = 48 km/hr.

The answers are different! The lesson is that speeds are measured, and measurements will always have independent and dependent variables that must be distinguished.

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