Question

If a man moves from one place to another at the speed of $4 \mathrm{~km} / \mathrm{hr}$ and comes back at the speed of $16 \mathrm{~km} / \mathrm{hr}$. Find the average speed of the man.

Answer 1

 Let the distance between one place to another be $x \mathrm{~km}$.

From the questions,

Total distance covered by a man $=x+x=2 x \mathrm{~km}$

Total time taken by the man

$$

=\frac{x}{4}+\frac{x}{16}=\frac{4 x+x}{16}=\frac{5 x}{16}

$$

$\therefore \quad$ Average speed

$$

\begin{array}{l}

=\frac{\text { Total distance }}{\text { Total time taken }} \\

=\frac{2 x}{\frac{5 x}{16}}=\frac{2 x \times 16}{5 x} \\

=\frac{32}{5}=6.4 \mathrm{~km} / \mathrm{hr} ; \text { Ans. }

\end{array}

$$

Trick :

Average speed $=\frac{2 \times 4 \times 16}{4+16}$

$$

\begin{array}{l}

=\frac{128}{20} \\

=6.4 km/hr 

\end{array}

$$