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
Concept. Average speed $=$ total distance / total time (not the simple average of speeds).
Step 1. Times. For a road $3d$ long: $t_1 = \dfrac{d}{12}$, $t_2 = \dfrac{2d}{18} = \dfrac{d}{9}$.
Step 2. Average speed.
$$v_{\text{avg}} = \frac{3d}{\frac{d}{12} + \frac{d}{9}} = \frac{3}{7/36} = \frac{108}{7} \approx 15.4\ \text{km/h}$$
Answer. $\dfrac{108}{7}$ km/h (Option A).
Solution by Sreeraj P, M.Sc Physics