BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Trains

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Master | Next Rank: 500 Posts
Posts: 184
Joined: Tue Sep 07, 2010 9:43 am
Thanked: 6 times
Followed by:1 members

Trains

by rahulvsd » Mon Apr 16, 2012 8:45 am
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

[spoiler]OA:B[/spoiler]
Top
Source: — Problem Solving |
User avatar
Legendary Member
Posts: 1239
Joined: Tue Apr 26, 2011 6:25 am
Thanked: 233 times
Followed by:26 members
GMAT Score:680

by sam2304 » Mon Apr 16, 2012 9:17 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.
Getting defeated is just a temporary notion, giving it up is what makes it permanent.
https://gmatandbeyond.blogspot.in/
Top
Junior | Next Rank: 30 Posts
Posts: 27
Joined: Sun Apr 08, 2012 5:38 am
Thanked: 20 times

by shubham_k » Mon Apr 16, 2012 9:17 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

Please take a moment to thank if this post was helpful
Top
Master | Next Rank: 500 Posts
Posts: 184
Joined: Tue Sep 07, 2010 9:43 am
Thanked: 6 times
Followed by:1 members

by rahulvsd » Mon Apr 16, 2012 9:50 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"
Top
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Mon Apr 16, 2012 10:31 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

[spoiler]OA:B[/spoiler]
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.

The correct answer is B.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
Senior | Next Rank: 100 Posts
Posts: 31
Joined: Sun Oct 16, 2011 10:02 am
Thanked: 4 times
Followed by:3 members

by gmatNooB8787 » Thu May 03, 2012 6:20 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 ?
Top
Post new topic Post Reply
• Page 1 of 1