Two trains of length 100m and 250m run on parallel lines : GMAT Problem Solving (PS)
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# Two trains of length 100m and 250m run on parallel lines

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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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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.
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Re: PS - Trains speed distance [#permalink]

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29 Sep 2009, 12:01
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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.
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Re: PS - Trains speed distance [#permalink]

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30 Sep 2009, 05:01
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AKprodigy87 - Nice clear response. Kudos
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Re: PS - Trains speed distance [#permalink]

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30 Sep 2009, 09:04
OA is 20m/s and 15m/s
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Re: PS - Trains speed distance [#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
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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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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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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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15 Oct 2013, 18:37
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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
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Re: Two trains of length 100m and 250m run on parallel lines [#permalink]

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07 Feb 2015, 09:36
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Re: Two trains of length 100m and 250m run on parallel lines [#permalink]

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12 Sep 2016, 18:37
Hello from the GMAT Club BumpBot!

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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] 12 Sep 2016, 19:06
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