Q 11-02-020NEETJEE MainMedium
A cyclist covers the first one-third of a straight road at $12$ km/h and the remaining two-thirds at $18$ km/h. His average speed for the whole road is
Answer: (A) $\dfrac{108}{7}$ km/h
Let the road be $3d$ long. Time for each part:
$$t_1 = \frac{d}{12}, \qquad t_2 = \frac{2d}{18} = \frac{d}{9}$$
$$v_{avg} = \frac{3d}{\dfrac{d}{12} + \dfrac{d}{9}} = \frac{3}{\dfrac{3 + 4}{36}} = \frac{108}{7} \approx 15.4\ \text{km/h}$$
Note that this is not the simple average $15$ km/h: the cyclist spends more time on the slower part.
Solution by Sreeraj P, M.Sc Physics