Question

A car travels the first third of a distance with a speed of $10kmph$, the second third at $20kmph$ and the last third at $60kmph$. What is its mean speed over the entire distance?

Answer 1

Let the total distance traveled be $s$.

Hence the time taken for first third of the distance= $t_1=\frac{s/3}{v_1}$

Similarly,the time taken for second third of the distance= $t_2=\frac{s/3}{v_2}$

and the time taken for last third of the distance= $t_3=\frac{s/3}{v_3}$

Hence the mean speed over the distance=$\frac{s}{t_1+t_2+t_3}$

$=\frac{3}{\frac{1}{v_1}+\frac{1}{v_2}+\frac{1}{v_3}}$

$=18km/h$