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# Two trains, X and Y, started simultaneously from opposite

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Two trains, X and Y, started simultaneously from opposite [#permalink]

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30 Nov 2010, 06:30
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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

OPEN DISCUSSION OF THIS QUESTION IS HERE: two-trains-x-and-y-started-simultaneously-from-opposite-en-168061.html
[Reveal] Spoiler: OA

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Last edited by Bunuel on 30 Apr 2014, 02:12, edited 2 times in total.
Renamed the topic and edited the question.

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30 Nov 2010, 06:40
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lets say they meet after X miles have been covered by T2..that means train 1 has travelled 100 -X miles in the same time

time taken by train 1 to cover 100 -X miles = (100 -X)/20
time taken by train 2 to cover X miles = X /(100/3) = 3X/100

(100 -X)/20 = 3X/100

which gives X = 62.5
which means train 1 had travelled 37.5
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30 Nov 2010, 07:32
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Train A's Speed 100/5 == 20 miles/hr
B's Speed 100/3 = 33.3 miles/hr

Relative speed 53.3 miles/hr

To cover 100 miles with relative speed time taken 100/53.3 almost 135 % of an hour

Train A will cover 135% of 20 approx 37.6

HTH

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30 Nov 2010, 10:34
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Train A speed = t1 = 20 mph
Train B speed= t2 = 100/3 mph
Combined speed(travelling towards each other) = 160/3 mph

When trains meet each other, they've covered 100 miles together.

Thus time = 100/(160/3) = 30/16 = 15/8 hours

out of 100 miles, distance covered by Train A = 20mph * 15/8 hours = 37.5 miles

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30 Nov 2010, 10:59
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ajit257 wrote:
Two trains X and Y started simultaneously from opposite ends of a 100 mile route and travelled toward each other on parallel tracks. Train X travelling at a constant rate completed the 100 mile trip in 5 hours. Train Y travelling at constant rate completed the 100 mile trip in 3 hours. How many miles had train X travelled when it met train Y ?

Can someone please explain the concept behind this type of problem ? All help appreciated.

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.

Time taken to meet = Total distance traveled/Relative speed

Speed of train X = 100/5 = 20 miles/hr
Speed of train Y = 100/3 miles/hr
Relative Speed = 20 + 100/3 = 160/3 miles/hr
Distance between them = 100 miles
Time taken to meet = 100/(160/3) hr = 15/8 hrs

In this time, train X would have traveled 20 * (15/8) = 37.5 miles

Faster Alternate Approach using Ratios :

Time taken by train X : Time taken by train Y = 5:3
Then, Speed of train X:Speed of train Y = 3:5
Since they start simultaneously, they travel for same time. So the ratio of their distance covered should be same as ratio of their speeds.
Distance covered by train X : Distance covered by train Y = 3:5
3/8 *100 = 37.5 miles (Distance covered by train X)
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Kudos [?]: 17770 [16], given: 235 Director Status: No dream is too large, no dreamer is too small Joined: 14 Jul 2010 Posts: 609 Kudos [?]: 1153 [0], given: 39 Two trains X and Y started simultaneously from opposite ends of a 100 [#permalink] ### Show Tags 17 Feb 2011, 12:12 3 This post was BOOKMARKED Two trains X and Y started simultaneously from opposite ends of a 100 mile route and travelled toward each other on parallel tracks. Train X travelling at a constant rate completed the 100 mile trip in 5 hours. Train Y travelling at constant rate completed the 100 mile trip in 3 hours. How many miles had train X travelled when it met train Y ? (A) 37.5 (B) 40.0 (C) 60.0 (D) 62.5 (E) 77.5 I solved as under Time taken to meet = Total distance traveled/Relative speed Speed of train X = 100/5 = 20 miles/hr Speed of train Y = 100/3 miles/hr Relative Speed = 20 + 100/3 = 160/3 miles/hr Distance between them = 100 miles Time taken to meet = 100/(160/3) hr = 15/8 hrs In this time, train X would have traveled 20 * (15/8) = 37.5 miles _________________ Collections:- PSof OG solved by GC members: http://gmatclub.com/forum/collection-ps-with-solution-from-gmatclub-110005.html DS of OG solved by GC members: http://gmatclub.com/forum/collection-ds-with-solution-from-gmatclub-110004.html 100 GMAT PREP Quantitative collection http://gmatclub.com/forum/gmat-prep-problem-collections-114358.html Collections of work/rate problems with solutions http://gmatclub.com/forum/collections-of-work-rate-problem-with-solutions-118919.html Mixture problems in a file with best solutions: http://gmatclub.com/forum/mixture-problems-with-best-and-easy-solutions-all-together-124644.html Kudos [?]: 1153 [0], given: 39 Director Status: -=Given to Fly=- Joined: 04 Jan 2011 Posts: 830 Kudos [?]: 247 [0], given: 78 Location: India Concentration: Leadership, Strategy Schools: Haas '18, Kelley '18 GMAT 1: 650 Q44 V37 GMAT 2: 710 Q48 V40 GMAT 3: 750 Q51 V40 GPA: 3.5 WE: Education (Education) Re: Two trains X and Y started simultaneously from opposite ends of a 100 [#permalink] ### Show Tags 17 Feb 2011, 18:42 Alternate Approach: Given: Speed of X = 20 mph Speed of Y = 33.33 mph Let the two trains meet at time 't' Distance travelled by X in time 't' be Dx Distance travelled by y in time 't' be Dy Since the time is equal, we can equate it: Dx/20 = Dy/33.33 or Dx*100/3 = Dy * 20 or 100Dx = 60Dy Dx+Dy=100 Multiply above equation with 60 60Dx + 60Dy = 6000 60Dx + 100Dx = 6000 [Since, 60Dy = 100Dx] 160Dx=6000 or Dx=6000/160 = 600/16 = (25*6)/4 = (25*3)/2 = 75/2 = 37.5 _________________ "Wherever you go, go with all your heart" - Confucius Useful Threads 1. How to Review and Analyze your Mistakes (Post by BB at GMAT Club) 2. 4 Steps to Get the Most out out of your CATs (Manhattan GMAT Blog) My Experience With GMAT 1. From 650 to 710 to 750 - My Tryst With GMAT 2. Quest to do my Best - My GMAT Journey Log Kudos [?]: 247 [0], given: 78 Director Status: -=Given to Fly=- Joined: 04 Jan 2011 Posts: 830 Kudos [?]: 247 [0], given: 78 Location: India Concentration: Leadership, Strategy Schools: Haas '18, Kelley '18 GMAT 1: 650 Q44 V37 GMAT 2: 710 Q48 V40 GMAT 3: 750 Q51 V40 GPA: 3.5 WE: Education (Education) Re: Two trains X and Y started simultaneously from opposite ends of a 100 [#permalink] ### Show Tags 17 Feb 2011, 18:44 Your approach is faster than the one I suggested But I just wanted to highlight the concept of equating time. _________________ "Wherever you go, go with all your heart" - Confucius Useful Threads 1. How to Review and Analyze your Mistakes (Post by BB at GMAT Club) 2. 4 Steps to Get the Most out out of your CATs (Manhattan GMAT Blog) My Experience With GMAT 1. From 650 to 710 to 750 - My Tryst With GMAT 2. Quest to do my Best - My GMAT Journey Log Kudos [?]: 247 [0], given: 78 Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7736 Kudos [?]: 17770 [1], given: 235 Location: Pune, India Re: Two trains X and Y started simultaneously from opposite ends of a 100 [#permalink] ### Show Tags 17 Feb 2011, 19:33 1 This post received KUDOS Expert's post 1 This post was BOOKMARKED Baten80 wrote: Two trains X and Y started simultaneously from opposite ends of a 100 mile route and travelled toward each other on parallel tracks. Train X travelling at a constant rate completed the 100 mile trip in 5 hours. Train Y travelling at constant rate completed the 100 mile trip in 3 hours. How many miles had train X travelled when it met train Y ? (A) 37.5 (B) 40.0 (C) 60.0 (D) 62.5 (E) 77.5 I solved as under Time taken to meet = Total distance traveled/Relative speed Speed of train X = 100/5 = 20 miles/hr Speed of train Y = 100/3 miles/hr Relative Speed = 20 + 100/3 = 160/3 miles/hr Distance between them = 100 miles Time taken to meet = 100/(160/3) hr = 15/8 hrs In this time, train X would have traveled 20 * (15/8) = 37.5 miles Another approach: Time taken by train X to cover 100 miles : Time taken by train Y to cover 100 miles = 5:3 Therefore, Speed of X: Speed of Y = 3:5 So, when they meet, X would have covered (3/8)th of the total distance of 100 miles. Distance covered by X = (3/8)*100 = 37.5 miles _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Re: Two trains X and Y started simultaneously from opposite ends of a 100 [#permalink]

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17 Feb 2011, 19:47
Good one Karishma

Didn't think of applying proportionality :D
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Re: Two trains X and Y started simultaneously from opposite ends of a 100 [#permalink]

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18 Feb 2011, 02:01
Let X traveled x miles at speed=(100/5) miles/h when they both met.
Y would have traveled (100-x) miles at speed=(100/3) miles/h

time spent by X = time spent by Y

time = Distance/speed

$$\frac{x}{\frac{100}{5}} = \frac{100-x}{\frac{100}{3}}$$

$$\frac{5x}{100} = \frac{3(100-x)}{100}$$

$$5x=300-3x$$

$$8x=300$$

$$x=37.5 miles$$

Ans: "A"
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28 Nov 2012, 19:10
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Faster Alternate Approach using Ratios :

Time taken by train X : Time taken by train Y = 5:3
Then, Speed of train X:Speed of train Y = 3:5
Since they start simultaneously, they travel for same time. So the ratio of their distance covered should be same as ratio of their speeds.
Distance covered by train X : Distance covered by train Y = 3:5
3/8 *100 = 37.5 miles (Distance covered by train X)

This is mind blowing
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Re: Two trains, X and Y, started simultaneously from opposite [#permalink]

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29 Nov 2012, 07:13
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As I can see, I notice different approachs that are good but not so efficient

$$relative rates : 5 + 3 = 8$$

$$RT= D$$----> $$\frac{100}{8}$$ $$= 12.5$$

Now this is a problem where the 2 times are dissimilar, is like a weigthed average in some how: what is the train that have more weigth in this scenario: the train with the 3 hours of trip.

So : $$12.5 * 3 = 37.5$$

A is the answer. This is the fastest approach you can do with these tricky problems. that's it
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Re: Two trains, X and Y, started simultaneously from opposite [#permalink]

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29 Apr 2014, 17:48
Hello from the GMAT Club BumpBot!

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

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30 Apr 2014, 02:12
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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

As the ratio of the rates of X and Y is 3 to 5 then the distance covered at the time of the meeting (so after traveling the same time interval) would also be in that ratio, which means that X would cover 3/(3+5)=3/8 of 100 miles: 100*3/8=37.5 miles.

OPEN DISCUSSION OF THIS QUESTION IS HERE: two-trains-x-and-y-started-simultaneously-from-opposite-en-168061.html
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Re: Two trains X and Y started simultaneously from opposite ends of a 100 [#permalink]

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25 Feb 2017, 12:16
Hello from the GMAT Club BumpBot!

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Re: Two trains X and Y started simultaneously from opposite ends of a 100   [#permalink] 25 Feb 2017, 12:16
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