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Two trains A and B left from two stations towards station B and statio

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Two trains A and B left from two stations towards station B and statio  [#permalink]

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New post 03 Jun 2019, 22:43
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Difficulty:

  65% (hard)

Question Stats:

55% (02:33) correct 45% (03:12) wrong based on 38 sessions

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Two trains A and B left from two stations towards station B and station A respectively. 3 hours after they met, the trains were 675 miles apart. The first train arrived at its destination 16 hours after their meeting and the second train arrived at its destination 25 hours after their meeting. How long did it take for the first train to make the whole trip?

A. 18 hours
B. 36 hours
C. 25 hours
D. 48 hours
E. 60 hours

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Re: Two trains A and B left from two stations towards station B and statio  [#permalink]

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New post 04 Jun 2019, 00:16
1
\(\frac{Velocity of A}{Velocity of B}\)= \(\sqrt{25/16}\)
\(\frac{Velocity of A}{Velocity of B}\)=5/4

Distance covered by train before the meeting is same as the distance covered by the second train after the meeting.
Time taken by train A before the meeting= 25*(4/5)=20 hrs
Time taken by train A for whole trip=20+16=36 hours


DisciplinedPrep wrote:
Two trains A and B left from two stations towards station B and station A respectively. 3 hours after they met, the trains were 675 miles apart. The first train arrived at its destination 16 hours after their meeting and the second train arrived at its destination 25 hours after their meeting. How long did it take for the first train to make the whole trip?

A. 18 hours
B. 36 hours
C. 25 hours
D. 48 hours
E. 60 hours
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Posts: 212
Re: Two trains A and B left from two stations towards station B and statio  [#permalink]

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New post 04 Jun 2019, 00:50
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1
A___________________M_____________B

In the above diagram, A and B denote the stations from which trains A and B start travelling towards each other and M their meeting point. Say they meet 't' hrs after they depart from their respective stations. Thus, in 't' hrs, Train A covers distance AM and Train B covers distance BM. It is given that the 1st train (A) covers BM in 16 hrs and the 2nd train (B) covers AM in 25 hrs. We know the ratio of the speeds of two moving objects is equal to the reciprocal of the times that each take to cover the same distance. Thus, if SA and SB are the speeds of A and B respectively then:

SA/SB=25/t (considering that it takes 't' hrs and 25 hrs for A and B respectively to cover AM).
Also, SA/SB=t/16 ( considering that it takes 16 hrs and 't' hrs for A and B respectively to cover BM).

Thus, 25/t=t/16---> t=20. Thus, Train A takes 20+16=36 hrs to cover the whole distance. Ans: B

P.S. It appears that the information that the two trains were 675 miles apart 3 hours after they met is superfluous.
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Re: Two trains A and B left from two stations towards station B and statio  [#permalink]

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New post 20 Jun 2020, 06:46
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Re: Two trains A and B left from two stations towards station B and statio   [#permalink] 20 Jun 2020, 06:46

Two trains A and B left from two stations towards station B and statio

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