A person X is running around a circular track | vedclass

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(B) Let the circumference of the circular track be $C$.Person $X$ completes one round in $40 \ s$. Therefore,the speed of $X$ is $v_X = \frac{C}{40} \

Vedclass · Accepted Answer

$24$

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(B) Let the circumference of the circular track be $C$.Person $X$ completes one round in $40 \ s$. Therefore,the speed of $X$ is $v_X = \frac{C}{40} \ m/s$.Let $Y$ complete one round in $t \ s$. Therefore,the speed of $Y$ is $v_Y = \frac{C}{t} \ m/s$.Since they are running in opposite directions,their relative speed is $v_{rel} = v_X + v_Y = \frac{C}{40} + \frac{C}{t}$.They meet every $15 \ s$,which means the total distance covered by both relative to each other in $15 \ s$ is one full circumference $C$.$v_{rel} 	imes 15 = C$$\left(\frac{C}{40} + \frac{C}{t}ight) 	imes 15 = C$Dividing both sides by $C$:$\left(\frac{1}{40} + \frac{1}{t}ight) 	imes 15 = 1$$\frac{1}{40} + \frac{1}{t} = \frac{1}{15}$$\frac{1}{t} = \frac{1}{15} - \frac{1}{40}$$\frac{1}{t} = \frac{8 - 3}{120} = \frac{5}{120} = \frac{1}{24}$$t = 24 \ s$.

$A$ person $X$ is running around a circular track,completing one round every $40 \ s$. Another person $Y$ running in the opposite direction meets $X$ every $15 \ s$. The time,expressed in seconds,taken by $Y$ to complete one round is

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