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

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Veritas Prep GMAT Instructor
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Two trains run in opposite directions on a circular track.  [#permalink]

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21 Sep 2014, 21:44
1
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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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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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.
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Re: Two trains run in opposite directions on a circular track.  [#permalink]

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31 Mar 2020, 08:26
alex1233 wrote:
Two trains run in opposite directions on a circular track. Train A travels at a rate of 4π miles per hour and Train B runs at a rate of 6π miles per hour. If the track has a radius of 6 miles and the trains both start from Point S at the same time, how long, in hours, after the trains depart will they again meet at Point S?

A. 3
B. 6
C. 9
D. 18
E. 22

Given: Two trains run in opposite directions on a circular track. Train A travels at a rate of 4π miles per hour and Train B runs at a rate of 6π miles per hour.

Asked: If the track has a radius of 6 miles and the trains both start from Point S at the same time, how long, in hours, after the trains depart will they again meet at Point S?

Relative speed = 10π miles per hour

Circumference of circular track = 2 π * 6 = 12π miles

Time taken by A to complete the track = 3 hours
Time taken by B to complete the track = 2 hours

Time when they will first meet = LCM (2,3) = 6 hours

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

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24 Apr 2020, 21:49
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

Sorry for dragging up an old post, but is this solution right? The objects are moving in opposite direction so relative speed should be sum of individual speeds right? Can relative speed be applied to solve such a problem?

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

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27 Apr 2020, 01:37
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rishi02 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

Sorry for dragging up an old post, but is this solution right? The objects are moving in opposite direction so relative speed should be sum of individual speeds right? Can relative speed be applied to solve such a problem?

This solution is correct and you are right too.

Yes, since the trains are moving in opposite directions, their "relative speed" will be sum of their speeds. But the concept of relative speed does not help us here because the trains need to meet back at point S. We can find the the trains will cover 1 full round together in 12π/10π hrs but they will not meet at S in this case.

The best way is to figure at what time each train comes to S and the common point when they both will be at S.

What is done in this solution is this:

Assume the trains are moving in same direction. Then in 1 hr, they will create a gap of 2π miles between them. In 2 hrs, they will create a gap of 4π miles between them and so on till in 6 hrs, they create a gap of 12π miles between them. So they would create a gap of one full circle and would both be back at S. In this time, one train would have made 2 full rounds and the other would have made 3 full rounds. Now think - does it matter in which direction the trains were moving?
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Re: Two trains run in opposite directions on a circular track.  [#permalink]

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30 May 2020, 10:12
Bunuel wrote:
alexpavlos wrote:
Two trains run in opposite directions on a circular track. Train A travels at a rate of 4π miles per hour and Train B runs at a rate of 6π miles per hour. If the track has a radius of 6 miles and the trains both start from Point S at the same time, how long, in hours, after the trains depart will they again meet at Point S?

A. 3
B. 6
C. 9
D. 18
E. 22

The circumference of the track is $$2\pi{r}=12\pi$$;

Train A will be at point S every $$\frac{12\pi}{4\pi}=3$$ hours;

Train B will be at point S every $$\frac{12\pi}{6\pi}=2$$ hours;

So, they will meet at point S for the first time in 6 hours (the least common multiple of 2 and 3).

Am I doing this correctly? This method has worked for other examples like this.

Since they're moving in opposite directions, subtract the speeds... 6pi-4pi= 2pi.. total distance of circle = 12pi. 12pi/2 = 6pi
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Re: Two trains run in opposite directions on a circular track.  [#permalink]

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30 May 2020, 12:23
I solved this qtn using relative speed.

Since the relative speed = 2π and distance to cover (perimeter) = 12π
Hence time = 6 hours
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Re: Two trains run in opposite directions on a circular track.   [#permalink] 30 May 2020, 12:23

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