Question

a car covers one - third of a distance at a speed of 10 km / h . the second one third at a speed of 20 km/ h and the last one third at a speed of 60 km /h . calculate average speed of the car over entire distance.

Answer 1

Dear Student,

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{whole}\mathrm{distance}\mathrm{travelled}\mathrm{be}\mathrm{x}\mathrm{km}\mathrm{and} \\ \mathrm{the}\mathrm{average}\mathrm{speed}\mathrm{of}\mathrm{car}\mathrm{for}\mathrm{the}\mathrm{whole}\mathrm{journey}\mathrm{be}\mathrm{y}\mathrm{km}/\mathrm{h} \\ \frac{{\displaystyle \raisebox{1ex}{$\mathrm{x}$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}}{10}+\frac{{\displaystyle \raisebox{1ex}{$\mathrm{x}$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}}{20}+\frac{{\displaystyle \raisebox{1ex}{$\mathrm{x}$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}}{60}=\frac{\mathrm{x}}{\mathrm{y}} \\ \frac{1}{30}+\frac{1}{60}+\frac{1}{180}=\frac{1}{\mathrm{y}} \\ \frac{6+3+1}{180}=\frac{1}{\mathrm{y}} \\ \mathrm{y}=\frac{180}{10}=18\mathrm{km}/\mathrm{h} \end{gathered}$$