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Intern  Joined: 13 May 2013
Posts: 20
Two trains 1& 2 start simultaneously and run on parallel  [#permalink]

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Difficulty:   45% (medium)

Question Stats: 68% (02:04) correct 32% (02:02) wrong based on 221 sessions

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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.
Verbal Forum Moderator B
Joined: 10 Oct 2012
Posts: 590
Re: Two trains 1& 2 start simultaneously and run on parallel  [#permalink]

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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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Senior Manager  S
Joined: 07 Sep 2014
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Re: Two trains 1& 2 start simultaneously and run on parallel  [#permalink]

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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.
Yale Moderator S
Joined: 05 May 2019
Posts: 117
Schools: Tuck, NYU Stern, Yale, LBS, INSEAD, ISB, MBS
GPA: 3
Re: Two trains 1& 2 start simultaneously and run on parallel  [#permalink]

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