Question

A car covers the first one-third of a distance x at a speed of $10\, km\, h^{-1}$, the second one-third at a speed of $20\, km\, h^{-1}$ and the last one-third at a speed of $60\, km \,h^{-1}$. Find the average speed of the car over the entire distance x.

• A. $10\, km\, h^{-1}$
• B. $12\, km\, h^{-1}$
• C. $18\, km\, h^{-1}$
• D. $20\, km\, h^{-1}$

Answer 1

The Correct Option is C

For first one-third of distance Distance covered $= \frac{x}{3} \,km$ Speed $= 10\,km\, h^{-1}.$ The time taken for the journey, $t_{1} = \frac{x/3}{10} h = \frac{x}{30} h$ For the next one-third of distance : Distance covered $= \frac{x}{3} km$ Speed $= 20\, km\, h^{-1}.$ The time taken for travel is $t_{2} = \frac{x/3}{20} h = \frac{x}{60} h$ For the last one-third of distance : Distance covered $= \frac{x}{3} \,km$ Speed $= 60 \,km\, h^{-1}.$ The time taken for travel is $t_{3} = \frac{x/3}{60} h = \frac{x}{180} h$ $\therefore\quad$ Average Speed $= \frac{total \,distance}{total\, time} = \frac{x}{\frac{x}{30}+\frac{x}{60}+\frac{x}{180}}$ $= \frac{180x}{10x} = 18\, km\, h^{-1}$