Question

A car travels $\frac{1}{3}$rd distance on a straight 3 road with a velocity of 10 km/hr, next $\frac{1}{3}$rd with velocity $20km/hr$ and the last $\frac{1}{3}$rd with velocity $60km/hr$. What is the average velocity of the car in the whole journey?

• A. $4km/hr$
• B. $6km/hr$
• C. $12km/hr$
• D. $18km/hr$

Answer 1

The correct option is D $18km/hr$

Let total distance of the journey be $s$ and be $t_1$, $t_2$ and $t_3$ be time taken for respective journeys, then

$t_1=s/(3\times v_1)=s/(3\times 10)=s/30$

$t_2=s/(3\times v_2)=s/(3\times 20)=s/60$

$t_3=s/(3\times v_3)=s/(3\times 60)=s/180$

Total time is

$t=t_1+t_2+t_3=s(1/30+1/60+1/180)=10s/180$

So average velocity is $v=s/t=s/\left(10s/180\right)=18km/hr$