A body covers the first $\frac{1}{3}$ part of its journey with the speed of $2m/s$, next $\frac{1}{3}$ part with the speed of 3 m/s and the rest of the journey with a speed $6m/s$. The average speed of the body will be

The correct option is A $3m/s$
Let the total distance covered be $d$ and the time taken in covering each part of the journey be $t_1$, $t_2$ and $t_3$ respectively.


As per the data shown in the figure, we have
$t_1=\frac{\frac{d}{3}}{v_1}=\frac{\frac{d}{3}}{2}=\frac{d}{6}$
And, $t_2=\frac{\frac{d}{3}}{v_2}=\frac{\frac{d}{3}}{3}=\frac{d}{9}$
And, $t_3=\frac{\frac{d}{3}}{v_3}=\frac{\frac{d}{3}}{6}=\frac{d}{18}$
$\therefore$ Avearge speed $=\frac{\text{Total distance covered}}{\text{Total time taken}}=\frac{d}{\frac{d}{6}+\frac{d}{9}+\frac{d}{18}}=\frac{18}{6}=3m/s$