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Two trains, X and Y, started simultaneously from opposite ends of a 10

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Re: Two trains, X and Y, started simultaneously from opposite ends of a 10  [#permalink]

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New post 13 Mar 2018, 05:15
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

Two trains, X and Y, started simultaneously from opposite ends of a 100-mile route and traveled toward each other on parallel tracks. Train X, traveling at a constant rate, completed the 100-mile trip in 5 hours; Train Y, traveling at a constant rate, completed the 100-mile trip in 3 hours. How many miles had Train X traveled when it met Train Y?

(A) 37.5
(B) 40.0
(C) 60.0
(D) 62.5
(E) 77.5

Problem Solving
Question: 119
Category: Algebra Applied problems
Page: 77
Difficulty: 600


GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

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Greetings everyone :)
Can anyone share some useful formulas like relative speed etc ? :)

many thanks! :-)
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Re: Two trains, X and Y, started simultaneously from opposite ends of a 10  [#permalink]

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New post 13 Mar 2018, 11:39
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dave13 wrote:
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

Two trains, X and Y, started simultaneously from opposite ends of a 100-mile route and traveled toward each other on parallel tracks. Train X, traveling at a constant rate, completed the 100-mile trip in 5 hours; Train Y, traveling at a constant rate, completed the 100-mile trip in 3 hours. How many miles had Train X traveled when it met Train Y?

(A) 37.5
(B) 40.0
(C) 60.0
(D) 62.5
(E) 77.5

Problem Solving
Question: 119
Category: Algebra Applied problems
Page: 77
Difficulty: 600


GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
1. Please provide your solutions to the questions;
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!


Greetings everyone :)
Can anyone share some useful formulas like relative speed etc ? :)

many thanks! :-)


Check out these two posts:
https://www.veritasprep.com/blog/2012/0 ... elatively/
https://www.veritasprep.com/blog/2012/0 ... -concepts/

They discuss relative speed in detail.
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Re: Two trains, X and Y, started simultaneously from opposite ends of a 10  [#permalink]

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New post 14 Apr 2019, 19:44
Step 1/3: Observe the outcome after 1 unit of time
After 1 hour, train X have traveled for 20 miles and train Y have traveled for 33.3 miles.

Step 2/3: Determine the shrink / expansion rate
The shrink rate is 20+33.3 = 53.3
It means that the distance between train X and train Y will shrink 53.3 miles, every 1 hour travel.

Step 3/3: Apply the shrink rate to the question
The question: How many miles had train X traveled when it met train Y?
If the shrink rate is 53.3 miles per hour, the total distance of 100 miles shall be shrunk in a little less than 2 hours. Train X is traveling at 20 miles per hour. A little less than 2 hours means a little less than 40 miles.
Only options A is possible.
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Re: Two trains, X and Y, started simultaneously from opposite ends of a 10  [#permalink]

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New post 01 Oct 2019, 18:31
relative speed of both
100/5+100/3 ; 800/15
so time taken ; 100/800 * 15 ; 15/8 hrs
so for train A distance ; 20*15/8 ; 75/2 ; 37.5 miles
IMO A



Bunuel wrote:
Two trains, X and Y, started simultaneously from opposite ends of a 100-mile route and traveled toward each other on parallel tracks. Train X, traveling at a constant rate, completed the 100-mile trip in 5 hours; Train Y, traveling at a constant rate, completed the 100-mile trip in 3 hours. How many miles had Train X traveled when it met Train Y?

(A) 37.5
(B) 40.0
(C) 60.0
(D) 62.5
(E) 77.5

Problem Solving
Question: 119
Category: Algebra Applied problems
Page: 77
Difficulty: 600


The Official Guide For GMAT® Quantitative Review, 2ND Edition
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Re: Two trains, X and Y, started simultaneously from opposite ends of a 10  [#permalink]

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New post 09 Dec 2019, 13:04
Bunuel wrote:
Two trains, X and Y, started simultaneously from opposite ends of a 100-mile route and traveled toward each other on parallel tracks. Train X, traveling at a constant rate, completed the 100-mile trip in 5 hours; Train Y, traveling at a constant rate, completed the 100-mile trip in 3 hours. How many miles had Train X traveled when it met Train Y?

(A) 37.5
(B) 40.0
(C) 60.0
(D) 62.5
(E) 77.5

Problem Solving
Question: 119
Category: Algebra Applied problems
Page: 77
Difficulty: 600


The Official Guide For GMAT® Quantitative Review, 2ND Edition



Time taken to meet = Total distance travelled/Relative speed

Speed of train X = 100/5 = 20 miles/hr
Speed of train Y = 100/3 = 33.3 miles/hr
Relative Speed = 20 + 33= 53 miles/hr
Distance between them = 100 miles
Time taken to meet = 100/(53) hr = 1.88 HR

bACK TO TARGET QUESTION'
How many miles had Train X traveled when it met Train Y?

dISTANCE TRAVELLED BY TRAIN X= 20 TIME =1.88
ANS= 20*1.88 =37.7 ANS A

The concept used in these questions is Relative Speed.

If two people walk in opposite directions (either towards each other or away from each other), their speed relative to each other is the sum of their speeds. e.g. If you are walking away from me at a speed of 2 miles/hr and I am walking away from you at a speed of 1 mile/hr, together we are creating a distance of 3 miles in 1 hr between us so our relative speed is 2 + 1 = 3 miles/hr
On the other hand, when two people walk in the same direction, their relative speed is the difference between their speeds.
e.g. if you are walking away from me at 1 mile/hr and I am walking towards you at 2 miles/hr, my speed relative to you is 2-1 = 1 mile/hr.
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Re: Two trains, X and Y, started simultaneously from opposite ends of a 10   [#permalink] 09 Dec 2019, 13:04

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