Question

A bus travelling the first one-third distance at a speed of ${10 \, km \, h^{-1}}$, the next one-third at ${20 \, km \, h^{-1}}$ and last one third at ${60 \, km \, h^{-1}}$. The average speed of bus is

• A. ${16 \, km \, h^{-1}}$
• B. ${18 \, km \, h^{-1}}$
• C. ${9 \, km \, h^{-1}}$
• D. ${48 \, km \, h^{-1}}$

Answer 1

Answer: (B)

${18 \, km \, h^{-1}}$

Answer 2

Here $v_1 = {10\, km\, h^{-1} for \, 1^{st} \, 1/3^{rd} \, distance}$
$v_2 = {20\, km\, h^{-1} for \, 2^{nd} \, 1/3^{rd} \, distance}$
$v_3 = {60\, km\, h^{-1} for \, 3^{rd} \, 1/3^{rd} \, distance}$
$v_{avg} = \frac{3 v_1 v_2 v_3}{v_1 v_2 + v_2 v_3 + v_3 v_1}$
$= \frac{3 \times 10 \times 20 \times 60}{10 \times 20 + 20 \times 60 + 60\times 10}$
$v_{avg} ={18 \, km \, h^{-1}}$