alphonsa wrote:
I had the same doubt as above.
Shouldn't we add the relative speed?
But the first post mentions that the relative speed is subtracted ?
Yes, when two objects run in opposite directions, their relative speed is given by adding the two speeds. But think what will \(12\pi/(4\pi + 6\pi)\) give us. It will give us the time taken by the two of them to complete one circle together. They will meet somewhere on the circle but not at the starting point in this much time.
For the two objects to meet again at the starting point, one object must complete one full circle more than the other object. In every hour, the train B - that runs at a speed of \(6\pi\) - covers \(2\pi\) extra miles compared with train A which runs at a speed of \(4\pi\). We want train B to complete one full circle more than train A. In how much time will train B cover \(12\pi\) (a full circle) more than train A? In \(12\pi/ 2\pi\) hrs = 6 hrs.
Or another way to think about it is this:
Time taken by train A to complete one full circle \(= 12\pi/4\pi = 3\) hrs
Time taken by train B to complete one full circle \(= 12\pi/6\pi = 2\) hrs
So every 3 hrs train A is at S and every 2 hrs train B is at S. When will they both be together at S?
train A at S -> 3 hrs, 6 hrs, 9 hrs
train B at S -> 2 hrs, 4 hrs, 6 hrs, 8 hrs
In 6 hrs - the first common time (the LCM of 3 and 2)
Answer (B)
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Karishma
Veritas Prep GMAT Instructor
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