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## Trains

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rahulvsd Really wants to Beat The GMAT!
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Trains Mon Apr 16, 2012 9:45 am
Elapsed Time: 00:00
• Lap #[LAPCOUNT] ([LAPTIME])
Two trains continuously travel between Washington DC and Baltimore, which is 120 miles away. They start simultaneously, train A at Washington and train B at Baltimore, and run at 30 and 90 mph respectively. The station turnaround times are negligible. What is the distance between the point where the trains meet for the first time and the point where they meet for the second time?

(A) 0
(B) 30 miles
(C) 60 miles
(D) 90 miles
(E) 120 miles

OA:B

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Mon Apr 16, 2012 10:17 am
Two trains separated by 120 miles

First meet will be at 30 miles from Washington as train A would have covered 30 miles towards baltimore and train B would have covered 90 miles from baltimore. Second meet would be at 60 miles from Washington as train would have covered another 30 towards Baltimore in one hour while train B would have reached washington (30 miles from the first meet point) and traveled back 60 miles in one hour (30 + 60). Difference between the two = 30 miles.

-----------------------------
30 60

Using formula:
When the two trains meet, both the trains would have traveled for same amount of time.
Let X be the meeting point.
time for train A to reach X = time for train B to reach X
x/30 = (120-x)/90
x = (120-x)/3
4x = 120
x = 30. The distance between any two meeting points would remain constant until the speed remains constant. So distance between 1st and 2nd meeting point will be 30. You can even cross check it for 3rd meeting point using the first method posted above.

IMO B.

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shubham_k Just gettin' started!
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Mon Apr 16, 2012 10:17 am
Let the trains meet after a time t, so distance travelled in time t hours by trains are 90t and 30t, also we should notice when the trains meet they would together have covered a distance equal to the distance between the destination i.e. 120 miles.

90t + 30t = 120 thus t=1 so trains meet after 1 hour. So trains meet at a point 30 miles from washington or 90 miles from baltimore.Now as the speed of the train is not changing the distance between the meet points shall also not change. So the distance between the meet points is also 30

rahulvsd Really wants to Beat The GMAT!
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Mon Apr 16, 2012 10:50 am
Shubam_K:

Does this logic always work: "As the speed of the train is not changing the distance between the meet points shall also not change"

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GMATGuruNY GMAT Instructor
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Mon Apr 16, 2012 11:31 am
rahulvsd wrote:
Two trains continuously travel between Washington DC and Baltimore, which is 120 miles away. They start simultaneously, train A at Washington and train B at Baltimore, and run at 30 and 90 mph respectively. The station turnaround times are negligible. What is the distance between the point where the trains meet for the first time and the point where they meet for the second time?

(A) 0
(B) 30 miles
(C) 60 miles
(D) 90 miles
(E) 120 miles

OA:B
Draw.
Since each rate is a multiple of 30, divide the distance into 30-mile intervals called X, Y and Z.

After 1 hour, the trains meet at X:
Wash.......X......Y......Z......Balt
[]----->A
.............. B<-----------[]

After 2 hours, the trains meet at Y:
Wash......X......Y......Z......Balt
-------[]-->A
<------[]
---------->B

X-Y = 30 miles.

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gmatNooB8787 Rising GMAT Star
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Thu May 03, 2012 7:20 pm
Hi GMATGuruNY,
I am a bit confused. How can you say

After 2 hours, the trains meet at Y:
Wash......X......Y......Z......Balt
-------[]-->A
<------[]
---------->B

How can we be sure that they meet up again after 1 hour.

The way i calculated was to note down the time the faster train will take to reach the end and then again how much time it will take to overtake the slower one after turn around and then add the two. It is very time consuming. But i am not able to understand your logic as to how you calculated that they will meet again in 1 hour ?

Also is there a generalized rule for two vehicles overtaking or meeting in same or opposing routes ?

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