## 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