If a body covers one-third of its total distance at speed $v_1$,the next one-third at speed $v_2$,and the last one-third at speed $v_3$,then the average speed will be:

$A$ car moving on a straight road covers one-third of the distance with $20 \, km/hr$ and the rest with $60 \, km/hr$. The average speed is .......... $km/hr$.

$A$ man walks on a straight road from his home to a market $2.5 \,km$ away with a speed of $5 \,km/h$. Finding the market closed,he instantly turns and walks back home with a speed of $7.5 \,km/h$. The average speed of the man over the interval of time $0$ to $40 \,min$ is equal to

Explain average velocity and average speed.

Explain clearly, with examples, the distinction between
$(a)$ magnitude of displacement over an interval of time, and the total length of path covered by a particle over the same interval.
$(b)$ magnitude of average velocity over an interval of time, and the average speed over the same interval. [Average speed of a particle over an interval of time is defined as the total path length divided by the time interval].
Show in both $(a)$ and $(b)$ that the second quantity is either greater than or equal to the first. When is the equality sign true? [For simplicity, consider one-dimensional motion only].

$A$ train travels from city-$A$ to city-$B$ with a constant speed of $18 \,ms^{-1}$ and returns back to city-$A$ with a constant speed of $36 \,ms^{-1}$. Find its average speed during the journey. (in $\,ms^{-1}$)