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A train travels first one third of the distance on a straight track with velocity$10km h^{-1}$ next one third with velocity $20 kmh^{-1}$ and the last portion with velocity $60 kmh^{-1}$. What is the average velocity of the train for the whole journey ?

$\begin{array}{1 1}(A)\;78\;km\;h^{-1}\\(B)\;18km\;h^{-1} \\(C)\;67\;km\;h^{-1} \\(D)\;45\;km\;h^{-1}\end{array} $

1 Answer

Let s kilometer be the total distance of the journey .
Suppose the time taken in hours to cover first one-third and the last one third of the journey be$t_1,t_2 $ and $t_2$ respectively . Then
$t_1= \large\frac{s/3}{10}$
$t_2= \large\frac{s/3}{20}$
$t_3= \large\frac{s/3}{10}$
Total time of journey $t=t_1+t_2+t_3$
$\qquad = \large\frac{s}{(3)(10)} +\frac{s}{(3)(20)}+\frac{s}{(3)(60)}$
$\qquad= \large\frac{s}{18} $$h$
Average velocity $= \large\frac{\text{total distance in km}}{\text{total time in h }}$
$\qquad= \large\frac{s}{(s/18)}$$=18 km\;h^{-1}$
Hence B is the correct answer.
answered Jul 18, 2014 by meena.p

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