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Two trains A and B starting from two points and travelling

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Two trains A and B starting from two points and travelling  [#permalink]

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New post 18 Nov 2013, 08:48
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Two trains A and B starting from two points and travelling in opposite directions, reach their destinations 9 hours and 4 hours respectively after meeting each other. If the train A travels at 80kmph, find the rate at which the train B runs.

(A) 40
(B) 60
(C) 120
(D) 80
(E) 100

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Re: Two trains A and B starting from two points and travelling  [#permalink]

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New post 18 Nov 2013, 21:38
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1
fra wrote:
Two trains A and B starting from two points and travelling in opposite directions, reach their destinations 9 hours and 4 hours respectively after meeting each other. If the train A travels at 80kmph, find the rate at which the train B runs.

(A) 40
(B) 60
(C) 120
(D) 80
(E) 100

Posted from my mobile device


Using Formula:

If two objects A and B start simultaneously from opposite points and, after meeting, reach their destinations in ‘a’ and ‘b’ hours respectively (i.e. A takes ‘a hrs’ to travel from the meeting point to his destination and B takes ‘b hrs’ to travel from the meeting point to his destination), then the ratio of their speeds is given by:
Sa/Sb = √(b/a)
i.e. Ratio of speeds is given by the square root of the inverse ratio of time taken.
Sa/Sb = √(4/9) = 2/3

This gives us that the ratio of the speed of A : speed of B as 2:3.
Since speed of A is 80 kmph, speed of B must be 80*(3/2) = 120 kmph

You can also do this question without using the formula. Check out this post for the method: http://www.veritasprep.com/blog/2013/04 ... -formulas/
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Karishma
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Re: Two trains A and B starting from two points and travelling  [#permalink]

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New post 19 Nov 2013, 02:55
VeritasPrepKarishma wrote:
fra wrote:
Two trains A and B starting from two points and travelling in opposite directions, reach their destinations 9 hours and 4 hours respectively after meeting each other. If the train A travels at 80kmph, find the rate at which the train B runs.

(A) 40
(B) 60
(C) 120
(D) 80
(E) 100

Posted from my mobile device


Using Formula:

If two objects A and B start simultaneously from opposite points and, after meeting, reach their destinations in ‘a’ and ‘b’ hours respectively (i.e. A takes ‘a hrs’ to travel from the meeting point to his destination and B takes ‘b hrs’ to travel from the meeting point to his destination), then the ratio of their speeds is given by:
Sa/Sb = √(b/a)
i.e. Ratio of speeds is given by the square root of the inverse ratio of time taken.
Sa/Sb = √(4/9) = 2/3

This gives us that the ratio of the speed of A : speed of B as 2:3.
Since speed of A is 80 kmph, speed of B must be 80*(3/2) = 120 kmph

You can also do this question without using the formula. Check out this post for the method: http://www.veritasprep.com/blog/2013/04 ... -formulas/


Can you please explain this a little more?

First, nothing is given in the question as to what are the destinations of each train. Are we to assume that the starting point of A is destination of B and vice-versa?

Second, the question also doesn't say whether the trains started at the same time, can we just assume that they did?
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Re: Two trains A and B starting from two points and travelling  [#permalink]

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New post 19 Nov 2013, 08:57
gmatprav wrote:
VeritasPrepKarishma wrote:
fra wrote:
Two trains A and B starting from two points and travelling in opposite directions, reach their destinations 9 hours and 4 hours respectively after meeting each other. If the train A travels at 80kmph, find the rate at which the train B runs.

(A) 40
(B) 60
(C) 120
(D) 80
(E) 100

Posted from my mobile device


Using Formula:

If two objects A and B start simultaneously from opposite points and, after meeting, reach their destinations in ‘a’ and ‘b’ hours respectively (i.e. A takes ‘a hrs’ to travel from the meeting point to his destination and B takes ‘b hrs’ to travel from the meeting point to his destination), then the ratio of their speeds is given by:
Sa/Sb = √(b/a)
i.e. Ratio of speeds is given by the square root of the inverse ratio of time taken.
Sa/Sb = √(4/9) = 2/3

This gives us that the ratio of the speed of A : speed of B as 2:3.
Since speed of A is 80 kmph, speed of B must be 80*(3/2) = 120 kmph

You can also do this question without using the formula. Check out this post for the method: http://www.veritasprep.com/blog/2013/04 ... -formulas/


Can you please explain this a little more?

First, nothing is given in the question as to what are the destinations of each train. Are we to assume that the starting point of A is destination of B and vice-versa?

Second, the question also doesn't say whether the trains started at the same time, can we just assume that they did?


The intent of the question is quite clear - the execution sure is lacking. In my post, I have explicitly mentioned both points as they will be in an actual GMAT question too.
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Karishma
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Re: Two trains A and B starting from two points and travelling  [#permalink]

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New post 19 Nov 2013, 10:00
VeritasPrepKarishma wrote:

The intent of the question is quite clear - the execution sure is lacking. In my post, I have explicitly mentioned both points as they will be in an actual GMAT question too.


Hello Karishma thanks for the reply. Yes, I checked your link and it is very clear about the destinations, the current question was not. I also arrived at the same answer going purely by the intent :) I wanted to make sure I am not assuming something that is not stated in the question. Glad to know the real GMAT will not have this kind of ambiguity.
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Re: Two trains A and B starting from two points and travelling   [#permalink] 19 Nov 2013, 10:00
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