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Two trains 1& 2 start simultaneously and run on parallel

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innocous
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Two trains 1& 2 start simultaneously and run on parallel [#permalink] New post   23 Nov 2013, 04:57
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Two trains 1& 2 start simultaneously and run on parallel tracks between stations A and B .They pass each other after after "t" hours from the start.How much time does the train 2 takes to cover the remaining distance after they pass each other?

1) speed of train 1 is 4 times the speed of train 2.

2) after passing each other train 1 takes 4 hours to complete the remaining distance between the stations.
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mau5
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Re: Two trains 1& 2 start simultaneously and run on parallel [#permalink] New post   24 Nov 2013, 01:27
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innocous wrote:
Two trains 1& 2 start simultaneously and run on parallel tracks between stations A and B .They pass each other after after "t" hours from the start.How much time does the train 2 takes to cover the remaining distance after they pass each other?

1) speed of train 1 is 4 times the speed of train 2.

2) after passing each other train 1 takes 4 hours to complete the remaining distance between the stations.


Let the speed of train 1 be\(v_1\) and that of train 2 be \(v_2\); the distance between A and B : 5d


From F.S 1, \(v_1 = 4*v_2.\).Thus,we know that the distance covered by train 1 and train 2 when they meet are in the ratio of 4:1. Hence, the distance covered by train 1 is 4d and that by train 2 is d. Thus time taken by train 2 to cover the remaining distance : \(\frac{4d}{v_2}\) Clearly Insufficient.

F.S 2 states that train 1 takes 4 hours to cover the remaining distance. We have no relation between the two speeds,hence clearly Insufficient.

Taking both together, we know that \(\frac{d}{v_1} = 4 hours \to \frac{d}{4v_2} = 4.\)

Thus, \(\frac{4d}{v_2}\) \(= 4*16 = 64 hours.\)

Sufficient.

C.
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abrakadabra21
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Re: Two trains 1& 2 start simultaneously and run on parallel [#permalink] New post   30 Aug 2016, 01:59
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Two trains 1& 2 start simultaneously and run on parallel tracks between stations A and B .They pass each other after after "t" hours from the start.How much time does the train 2 takes to cover the remaining distance after they pass each other?

1) speed of train 1 is 4 times the speed of train 2.

2) after passing each other train 1 takes 4 hours to complete the remaining distance between the stations.

what train 2 has taken to cover, train 1 will take 1/4 th of it so in 1 hr they will meet.
so before meeting at the somewhere in between A & B, train 2 took 1 hr. that 1 hr will be 15 minute for train 1.
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Re: Two trains 1& 2 start simultaneously and run on parallel [#permalink] New post   01 Oct 2019, 07:39
Given - The time taken for both trains to meet = t hours.
Assuming the speed of T1 = V1 and speed of T2 = V2.
The total distance between the 2 stations = X
Distance travelled by T1 = P and Distance travelled by T2 = X - P.

Find the time T2 taskes to travel distance P.

Statement 1 - V1 = 4V2
P > X - P
This also means that V1 and V2 are in ratio 4/1. As for Distance travelled,
P = V1 x t. and X - P = V2 x t.
The value of P clearly can't be obtained from these two equations. The time T2 takes after the trains meet can't be found either. INSUFFICIENT. Options A & D eliminated.

Statement 2 - T1 -> 4 hours to complete the remaining distance X-P.
4 x V1 = X-P
But, Statement 2 doesn't give us a relationship between V1 and V2. INSUFFICIENT.
Option B now eliminated too.

Combining Statements 1 & 2,
We have -> P = V1 x t and X - P = V2 x t.
4 x V1 = X - P

Equating the values of X - P
=> 4V1 = V2t
=> 16V2 = V2t
=> t = 16 Hours.

Thus, the time taken for both trains to meet is equal to 16 hours.
We need not calculate further as to how much time T2 will take to cover distance P.
(1) & (2) are sufficient.

Answer is C.
GMAT Club Bot
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Re: Two trains 1& 2 start simultaneously and run on parallel [#permalink]
01 Oct 2019, 07:39
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