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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?

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

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17 Feb 2011, 12:12

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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
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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
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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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hope is a good thing, maybe the best of things. And no good thing ever dies.

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

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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.

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!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
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