3.20 Wighted AM vs Weighted HM

Suppose, a bus travels 10 km at 10 kph, another 15 km at 20 kph, and another 20 km at 25 kph. What is the average speed.

HM \(\rightarrow\) consider distances as weights

AM \(\rightarrow\) consider times as weights

Time, \(t=\frac d v=\) 1, 0.75, 0.8

• \(WHM = \frac{10+15+20}{\frac{10}{10}+\frac{15}{20}+\frac{20}{25}}\)=17.65
• \(WAM = \frac{1\times 10 + 0.75 \times 20 + 0.80 \times 25}{1+0.75+0.80}\) = 17.65
• True mean, \(\bar v=\frac{\sum d}{\sum t}=\frac{45}{2.55}=\) 17.65