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

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Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7799

Kudos [?]: 18149 [1], given: 236

Location: Pune, India
Two trains run in opposite directions on a circular track. [#permalink]

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21 Sep 2014, 21:44
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Expert's post
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.
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Re: Two trains run in opposite directions on a circular track. [#permalink]

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16 Jan 2015, 21:16
A = 4pi mph
B = 6pi mph
Relative speed = 2pi mph (objects in opposite direction hence subtract)
r = 6 mi
Circumference = Distance = 12pi

Using D = RT:
12pi = 2pi*T
T = 6

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Joined: 09 Feb 2013
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Re: Two trains run in opposite directions on a circular track. [#permalink]

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29 Aug 2017, 03:50
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 ?

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Joined: 22 May 2016
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Two trains run in opposite directions on a circular track. [#permalink]

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30 Aug 2017, 11:42
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 ?

kshitij89 , yes, you are correct.

VeritasPrepKarishma

Quote:
Yes, when two objects run in opposite directions, their relative speed is given by adding the two speeds
here:

https://gmatclub.com/forum/two-trains-run-in-opposite-directions-on-a-circular-track-132630.html#p1417394

See this post, too:

https://gmatclub.com/forum/two-trains-run-in-opposite-directions-on-a-circular-track-132630.html#p1418111

Maybe re-read the whole thread? Rates aren't the best method to solve this problem.

Hope that helps.

Kudos [?]: 407 [0], given: 647

Two trains run in opposite directions on a circular track.   [#permalink] 30 Aug 2017, 11:42

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