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Two racers are running to and fro from points $A$ and $B$ at $3m/s$ and $7m/s$ respectively. If the distance between $A$ and $B$ is $2000m$, what is the total distance covered by both the racers, till they meet for the $2^{nd}$ time?

Let $P$ and $Q$ be the racers who start from $A$ and $B$ respectively.

The first time they will meet at $600m$ away from $A$.

But I am getting confused how to determine whether for the second time when they will meet, will $P$ be able to reach $B$ or not? How can we determine that?

I also tried to solve this question by considering this race along a circular track where both the runners are running along opposite direction but in that I am getting $4000m$ as the answer.
As they will be running in opposite directions, there will be $10$ distinct meeting points which will be $200m$ apart. Now once they will meet for the first time along the circular track, after that I assumed that to be the starting point of the race and then found out the next meeting point from there and like this I got to the answer of $4000m$.

Thanks in advance !!!

Ganit
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1 Answers1

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When they meet the first time, the total distance they cover is the distance from A to B, which is 2000m. However, the second time, the additional distance they cover until they meet would be 2 times the distance from A to B, or 4000m (try to draw it out on a line with different colors and you will see why this is true). Thus, the total distance is 6000m.

Notice that in these types of questions that ask for the total sometimes you don't even need to know the speeds of the racers.

Fatso Boo
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