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(C) Let the total distance between $P$ and $Q$ be $3x \, km$.The distance is divided into three equal parts,each of length $x \, km$.For the first par

Vedclass · Accepted Answer

$18$

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(C) Let the total distance between $P$ and $Q$ be $3x \, km$.The distance is divided into three equal parts,each of length $x \, km$.For the first part,the speed is $v_1 = 10 \, km/h$. The time taken is $t_1 = \frac{x}{10} \, h$.For the second part,the speed is $v_2 = 20 \, km/h$. The time taken is $t_2 = \frac{x}{20} \, h$.For the third part,the speed is $v_3 = 60 \, km/h$. The time taken is $t_3 = \frac{x}{60} \, h$.The average speed is defined as the total distance divided by the total time taken:$	ext{Average Speed} = \frac{	ext{Total Distance}}{	ext{Total Time}} = \frac{3x}{t_1 + t_2 + t_3}$Substituting the values:$	ext{Average Speed} = \frac{3x}{\frac{x}{10} + \frac{x}{20} + \frac{x}{60}}$Taking the common denominator $(60)$:$	ext{Average Speed} = \frac{3x}{\frac{6x + 3x + x}{60}} = \frac{3x}{\frac{10x}{60}} = \frac{3x 	imes 60}{10x} = 18 \, km/h$.

$A$ person goes from point $P$ to point $Q$ covering $1/3$ of the distance with speed $10 \, km/h$,the next $1/3$ of the distance at $20 \, km/h$,and the last $1/3$ of the distance at $60 \, km/h$. The average speed of the person is ............ $km/h$.

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