Vetrik wrote:

Karishma,

The right method should be finding the LCM only for the trains have to meet at the same point. In the 3 Pi & 5 Pi problem, the trains will meet at the same point in 15 hrs.

Adding speeds can give the time at which they meet but not at the same meet e.g. in the 4 Pi & 6 Pi problem, the trains will first meet 1.2 hrs from the starting time i.e the 4 Pi train would have traveled 4.8Pi km & the 6Pi tarin would have traveled 7.2Pi kms [the total distance is 12Pi]

[Only if the trains travel in the same direction, the speeds should be subtracted...and again only the catch up time can be calculated from this. To get the time at which they will meet at the same point, LCM is the route]

??

The method of "dividing the distance by difference of the speed" is not necessarily wrong. In the \(3\pi\) and \(5\pi\) problem, the circumference of the circle is \(15\pi\). Train B gets ahead of train A by \(2\pi\) every hour. After 7.5 hours, it is \(15\pi\) ahead but it is not at S at that time because it reaches S in only integral hours. So train B needs to complete 2 full circles more than train A which it will do in 15 hours. In 15 hours, both trains will be at S.

_________________

Karishma

Private Tutor for GMAT

Contact: bansal.karishma@gmail.com