Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Two trains of length 100m and 250m run on parallel lines [#permalink]
29 Sep 2009, 10:55

2

This post received KUDOS

2

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

5% (low)

Question Stats:

56% (02:41) correct
44% (01:24) wrong based on 6 sessions

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.

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.

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

Re: Two trains of length 100m and 250m run on parallel lines [#permalink]
29 Mar 2012, 00:03

3

This post received KUDOS

Expert's post

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.

Re: Two trains of length 100m and 250m run on parallel lines [#permalink]
29 Mar 2012, 00:47

Expert's post

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?

Thnx in advance.

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.

Re: Two trains of length 100m and 250m run on parallel lines [#permalink]
15 Oct 2013, 18:37

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.

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

gmatclubot

Re: Two trains of length 100m and 250m run on parallel lines
[#permalink]
31 Dec 2013, 05:41