Question

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

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

Answer 1

Answer: (B)

Here $v_1=10km{h}^{-1}$ for $1^{\text{st }}\frac{1}{3}{}^{\text{rd }}$
distance $v_2=20km{h}^{-1}$ for $2^{\text{nd }}{\frac{1}{3}}^{\text{rd }}$
distance $v_3=60km{h}^{-1}$ for $3^{\text{rd }}{\frac{1}{3}}^{\text{rd }}$
distance $v_{\text{avg }}=\frac{3v_1{v}_2{v}_3}{v_1{v}_2+v_2{v}_3+v_3{v}_1}$
$=\frac{3\times 10\times 20\times 60}{10\times 20+20\times 60+60\times 10}$ $v_{avg}=18km{h}^{-1}$