A and B run a 5, km race on a round course of | vedclass

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(D) The ratio of the speeds of $A$ and $B$ is $5:4$. This means that in the same time interval,$A$ covers $5$ units of distance while $B$ covers $4$ u

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$2 \frac{1}{2}$ times

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(D) The ratio of the speeds of $A$ and $B$ is $5:4$. This means that in the same time interval,$A$ covers $5$ units of distance while $B$ covers $4$ units.In a circular race,the winner passes the other person when the difference in the number of laps completed by them is an integer.Since the ratio of their speeds is $5:4$,for every $5$ laps completed by $A$,$B$ completes $4$ laps. The difference in laps is $5 - 4 = 1$ lap.This means $A$ laps $B$ once for every $5$ laps $A$ completes.The total distance of the race is $5\, km = 5000\, m$. The length of one lap is $400\, m$.Total laps completed by $A = \frac{5000}{400} = 12.5$ laps.Since $A$ laps $B$ once every $5$ laps,the number of times $A$ passes $B$ is $\frac{12.5}{5} = 2.5$ or $2 \frac{1}{2}$ times.

$A$ and $B$ run a $5\, km$ race on a round course of $400\, m$. If their speeds are in the ratio $5:4$,how often does the winner pass the other?

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