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# Two trains of length 100m and 250m run on parallel lines

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Manager
Joined: 14 Dec 2008
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Two trains of length 100m and 250m run on parallel lines  [#permalink]

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29 Sep 2009, 10:55
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Difficulty:

55% (hard)

Question Stats:

55% (02:12) correct 45% (02:16) wrong based on 104 sessions

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Two trains of length 100m and 250m run on parallel lines. when they run in the same direction it will take 70 sec to cross each other and when they run in opposite direction, they take 10 sec to cross each other. Find the speed of faster train.

A. 10 m/s
B. 15 m/s
C. 20 m/s
D. 25 m/s
E. 30 m/s
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Re: Two trains of length 100m and 250m run on parallel lines  [#permalink]

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29 Mar 2012, 00:03
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manojgmat wrote:
Two trains of length 100m and 250m run on parallel lines. when they run in the same direction it will take 70 sec to cross each other and when they run in opposite direction, they take 10 sec to cross each other. find the speed of faster train.

Alternative approach:

To cross each other (either in same or opposite direction), the trains have to cover a distance of 250 + 100 = 350 m (the faster train should cover the entire slower train and then its own length so that they completely cross each other)

When they run in the same direction, they cover this distance in 70 sec. So their relative speed in this case (which is the difference in their speeds) is 350/70 = 5 m/s
When they run in opposite directions, they cover this distance in 10 sec. So their relative speed in this case (which is the sum of their speeds) is 350/10 = 35 m/s

If sum if 35 and difference is 5, you should quickly jump to 20 and 15.

Note: We used the concept of relative speed here.
When 2 objects move in same direction, their relative speed i.e. speed relative to each other is the difference of their speeds.
When the 2 objects move in opposite directions, their relative speed i.e. speed relative to each other is the sum of their speeds.
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Manager
Joined: 11 Sep 2009
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Re: Two trains of length 100m and 250m run on parallel lines  [#permalink]

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29 Sep 2009, 12:01
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The answer is 20 m/s.

Let the faster train run at x m/s and the slower train run at y m/s.

The first statement states that it will take 70 seconds to cross each other running in the same direction. The first important thing her is that the faster train is behind the slower train, otherwise they would never cross. Secondly, in order to cross the slower train, the faster train will need to cover 350m MORE (250 m + 100 m) in the 70 seconds than the other train.

$$\frac{350}{(x - y)} = 70$$

$$\frac{5}{(x - y)} = 1$$

$$5 = x - y$$ (Equation 1)

The second statement states that it will take 10 seconds to cross each other running in the opposite direction. The difference between this and running in the same direction, is that the slower train's speed CONTRIBUTES to the cross rather than inhibiting it. If the slower train was standing still, the faster train would take (350/x) seconds to pass it. Since the slower train is moving in the other direction though, it will take (350/ x+y) seconds to cross.

$$\frac{350}{(x + y)} = 10$$

$$\frac{35}{(x + y)} = 1$$

$$35 = x + y$$ (Equation 2)

Solving these two equations, you get x = 20 m/s, and y = 15 m/s.
##### General Discussion
Manager
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Re: Two trains of length 100m and 250m run on parallel lines  [#permalink]

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13 Mar 2012, 05:44
relative speeds: $$\frac{350}{70}=5$$ and $$\frac{350}{10}=35$$

$$a+b=35$$, $$a-b=5$$

20m/s and 15m/s
Intern
Joined: 03 Dec 2010
Posts: 21
Re: Two trains of length 100m and 250m run on parallel lines  [#permalink]

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28 Mar 2012, 21:58
Hello,

Though the explanation to the given problem is simple, could someone explain with example, as I still find it difficult to intrepret, which train is 100m and which one is 250 m long?

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Joined: 02 Sep 2009
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Re: Two trains of length 100m and 250m run on parallel lines  [#permalink]

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29 Mar 2012, 00:47
priyalr wrote:
Hello,

Though the explanation to the given problem is simple, could someone explain with example, as I still find it difficult to intrepret, which train is 100m and which one is 250 m long?

We can not deduce whether 100m train or 250m train is faster, we just know that the rate of a faster train, whichever it is, is 20 m/s and and the rate of a slower train is 15 m/s.

So, as you can see we can answer the question even not knowing whether 100m train or 250m train is faster. Refer to ANY solution above (they are basically all the same) to see how it can be done.

Hope it helps.
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Re: Two trains of length 100m and 250m run on parallel lines  [#permalink]

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31 Dec 2013, 05:41
manojgmat wrote:
Two trains of length 100m and 250m run on parallel lines. when they run in the same direction it will take 70 sec to cross each other and when they run in opposite direction, they take 10 sec to cross each other. find the speed of faster train.

We have

(a-b)(70) = (a+b)(10)

3a = 4b

We also know that (a-b)(70) = 350m
a-b =5

So a=20, b=15

The speed of the faster train is 20m/sec

Hope it helps
Cheers!
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Re: Two trains of length 100m and 250m run on parallel lines  [#permalink]

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12 Sep 2016, 19:06
I thought too much, and figured out it be only 150 m to cross the other train in the same direction, if they start at the same time and if the longer train is faster

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Re: Two trains of length 100m and 250m run on parallel lines  [#permalink]

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04 Sep 2019, 02:46
ProfX wrote:
I thought too much, and figured out it be only 150 m to cross the other train in the same direction, if they start at the same time and if the longer train is faster

Sent from my iPhone using GMAT Club Forum mobile app

I have the same question like yours. if they start at the same time, we have to assume that the shorter train is the faster one and the shorter need to cover only 150 m in order to catch up with the longer one.
Bunuel can you please clarify this for me?
Thank you in advance!
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Re: Two trains of length 100m and 250m run on parallel lines  [#permalink]

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13 Apr 2020, 20:59
I believe that, although the question isn’t entirely clear at first, when they go in the same direction, one train starts immediately behind the other train (don’t think it matters which train). Now the faster train has to make up the entire distance of the other train, plus get itself completely ahead of the other train in order to “cross”.

If the 100 meter train starts immediately behind the 250 meter train (and assuming the 100 meter train is faster), it must catch up through the 250 meter length of the other train. And also put its 150 meter length in front of the other train.

Am I correct in the way I’m interpreting the question?

It could also be the other way around, in which the 250 meter train is faster and starts out immediately behind the slower 100 meter train. Still going to be 350 meters until the entire train “crosses” the other train.

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Re: Two trains of length 100m and 250m run on parallel lines  [#permalink]

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13 Apr 2020, 21:01
Typo. “And also put its 100 meter length...”

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Re: Two trains of length 100m and 250m run on parallel lines   [#permalink] 13 Apr 2020, 21:01

# Two trains of length 100m and 250m run on parallel lines

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