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Re: Two trains run in opposite directions on a circular track. [#permalink]

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20 Sep 2014, 10:24

Ok...now what happens when the speed of the two trains are subtracted and the circumference distance is divided by that value.

Here what we are really finding out is the time taken for one of the trains to run one full circle more than the other train. i.e. when the speeds of trains are 4 Pi & 6 Pi...in 6 hrs [12 Pi / 2 Pi] one train travels 24 Pi miles and the other travels 36 Pi miles i.e. one train does 2 two rounds and the other train does 3 rounds.

Similarly when the speeds are 3 Pi & 5 Pi...in 7.5 hrs [15Pi/ 2 Pi] one train travels 22.5 miles and the other train travels 37.5 miles [15 miles more than the other] i.e. one train does 2.5 rounds and the other trains does 3.5 rounds.

It is only coincidental that this 6 hrs and the 6 hrs for the meeting time at the same point are equal....and hence LCM route is the right route.

Re: Two trains run in opposite directions on a circular track. [#permalink]

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21 Sep 2014, 02:05

Try the same question with speed of the trains as 3\pi and 5\pi and radius of the circle as 7.5 miles. The two methods give different answers - figure out why!

Method 1

Ratio of speed of Train A and Train B is 3:5. Considering the circle as 8 units, the 1st meeting point is 3 units away from starting point. For A & B to meet first time at starting point, we find lowest common multiple of 3 and 8 i.e. 24 units; thus, they must meet (24 units/3 units) 8 times. Time for each meet = \((\frac{15}{8})hrs\) Or time to meet 8th time=\((\frac{15}{8})*8=15 hrs.\)

Method 2

For the two objects to meet again at the starting point, one object must complete one full circle more than the other object . However, in order to satisfy the meeting point to be same as starting point, it is necessary that the difference of distance covered is a exact multiple of full circular distance. Relative speed per hr =\(2\pi\) Total circular distance =\(15\pi\) LCM of relative speed and circular distance =\(30\pi\) Or, Time to meet at starting point = \(\frac{30\pi}{2\pi per hr} =15 hrs\)

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.
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Re: Two trains run in opposite directions on a circular track. [#permalink]

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19 Jan 2016, 06:17

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Re: Two trains run in opposite directions on a circular track. [#permalink]

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14 Jul 2017, 00:48

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Re: Two trains run in opposite directions on a circular track. [#permalink]

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29 Aug 2017, 04:50

RSG wrote:

The trains will travel the perimeter of the circle which is 12π miles. The relative speed of the trains is 2π miles per hour. Time taken to meet = 12π/2π = 6 hours

When two trains are running in opposite direction, the relative speeds are added . Am I correct here ?

Two trains run in opposite directions on a circular track. [#permalink]

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30 Aug 2017, 12:42

kshitij89 wrote:

RSG wrote:

The trains will travel the perimeter of the circle which is 12π miles. The relative speed of the trains is 2π miles per hour. Time taken to meet = 12π/2π = 6 hours

When two trains are running in opposite direction, the relative speeds are added . Am I correct here ?

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