3.17 Story of Oil Scam

S = 150 km

\(v_1=\space 10 km/h, v_2=\space 15 km/h, v_3=\space 20 km/h\)

What is the average speed?

• \(AM=\frac{10+15+20}{3}=15 \space km/h\)
• Think more fundamentally
• \(\sum S=3\times 150=450\)
• \(t_1=15h, t_2=10h, t_3=7.5h\)
• \(\bar v = \frac{\sum S}{\sum t}=\frac{450}{32.5}=13.84 \lt AM\)

• \(=\frac{450}{15+10+7.5}\)
• \(=\frac{450}{\frac{150}{10}+\frac{150}{15}+\frac{150}{20}}\)
• \(=\frac{450}{150(\frac{1}{10}+\frac{1}{15}+\frac{1}{20})}\)
• \(=\frac{3}{\frac{1}{10}+\frac{1}{15}+\frac{1}{20}}\)
• \(=\frac{3}{\frac{1}{v_1}+\frac{1}{v_2}+\frac{1}{v_3}}\)