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

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Manager
Joined: 22 Nov 2016
Posts: 229
Location: United States (CA)
Concentration: Leadership, Strategy
GMAT 1: 640 Q43 V35
GPA: 3.4
WE: Design (Other)
Re: Two trains, X and Y, started simultaneously from opposite ends of a 10  [#permalink]

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25 Jun 2017, 14:31

I like to sketch out the problem and many times it is a fast method.

As you can see train A meets train B somewhere between the 20 and 40th mile. Looking at the answer choices, it is pretty obvious that A is the answer.
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Joined: 09 Mar 2016
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Re: Two trains, X and Y, started simultaneously from opposite ends of a 10  [#permalink]

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13 Mar 2018, 04:15
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

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

many thanks!
Intern
Joined: 01 Feb 2019
Posts: 13
Re: Two trains, X and Y, started simultaneously from opposite ends of a 10  [#permalink]

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14 Apr 2019, 18:44
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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01 Oct 2019, 17:31
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
Manager
Joined: 03 Aug 2017
Posts: 102
Re: Two trains, X and Y, started simultaneously from opposite ends of a 10  [#permalink]

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09 Dec 2019, 12:04
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.
Re: Two trains, X and Y, started simultaneously from opposite ends of a 10   [#permalink] 09 Dec 2019, 12:04

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

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