Question:
A motorcyclist drives from $A$ to $B$ with a uniform speed of $30 \mathrm{~km} \mathrm{~h}^{-1}$ and returns back with a speed of $20 \mathrm{~km}$ $\mathrm{h}^{-1}$. Find its average speed.
Solution:
Let, distance between $\mathrm{A}$ and $\mathrm{B}=x$. Time taken to go from $\mathrm{A}$ to $\mathrm{B}, t_{1}=\frac{x}{30} h$
Time taken to go from $\mathrm{B}$ to $\mathrm{A}, t_{2}=\frac{x}{20} b$
$\therefore v_{a v}=\frac{\text { Total distance }}{\text { Total time }}=\frac{2 x}{t_{1}+t_{2}}=\frac{2 x}{\frac{x}{30}+\frac{x}{20}}=24 \mathrm{~km} / \mathrm{h}$
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