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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.

Solution

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

$$\begin{array}{l} =\frac{128}{20} \\ =6.4 km/hr \end{array}$$

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