Average speed of the two cars approaching each other from opposite direction is calculated by which of the following ?

Question

Accepted Answer

The correct option is 3:

The average speed in scenarios involving distance and time is generally calculated using the Harmonic Mean (HM). This statistical measure is specifically used when rates or ratios are being averaged, and the two observations (in this case, the two speeds, $S_1$ and $S_2$) cover the same distance. The average speed ($S_{avg}$) is defined as Total Distance traveled divided by Total Time taken. When two cars approach each other and we want to find their combined average speed, the Harmonic Mean provides the correct formula for the weighted average of rates, given by $HM = \frac{n}{\frac{1}{S_1} + \frac{1}{S_2} + ... + \frac{1}{S_n}}$. For two speeds, this simplifies to $\frac{2 \cdot S_1 \cdot S_2}{S_1 + S_2}$, which accurately represents the overall rate of movement when distances are equal, or when we are considering their relative speed over a fixed total path.

The incorrect option is 1:
The Arithmetic Mean (AM) is used when finding the average of quantities that cover equal time periods, not equal distances or rates. Calculating the AM of speeds would simply be $\frac{S\_1 + S\_2}{2}$, which incorrectly represents the average speed unless the time taken by both vehicles was identical.

The incorrect option is 2:
The Geometric Mean (GM) is typically used when finding the average of rates of change, percentages, or growth rates over a period, such as in finance or biological studies. It is mathematically inappropriate for calculating the average speed when equal distance is involved.

The incorrect option is 4:
Mechanical mean is not a recognized or standard statistical measure used for calculating averages in physics or economics. The term is likely a distracter and has no conceptual relevance to finding the average speed of moving objects.