Question

A car travels first $\frac{1}{3}$ of the distance AB at $30km/h$,next$\frac{1}{3}$ of the distance at $40km/h$ and last $\frac{1}{3}$ of the distance at $24km/h$ Its average speed in km/h for the whole journey is

• A. $40$
• B. $35$
• C. $30$
• D. $28$

Answer 1

The correct option is C $30$

Total distance covered by a car is, $AB=d=\frac{1}{3}+\frac{1}{3}+\frac{1}{3}=1km$

A car travels first $\frac{1}{3}$ of distance $AB$ at speed $30km/h$, then

$t_1=\frac{1}{3\times 30}=\frac{1}{90}hr$

Next $\frac{1}{3}$ of $AB$ with speed $40km/h$, then

$t_2=\frac{1}{3\times 40}=\frac{1}{120}hr$

Last $\frac{1}{3}$ with speed $24km/h$, then

$t_3=\frac{1}{3\times 24}=\frac{1}{72hr}$

Total time, $t=t_1+t_2+t_3$

$t=\frac{1}{90}+\frac{1}{120}+\frac{1}{72}=0.0334hr$

The average speed of the car,

$v_{avg}=\frac{Totaldistance}{Totaltime}$

$v_{avg}=\frac{1}{0.033}=30km/h$

The correct option is C.