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Two trains traveling toward each other on parallel tracks at constant

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Two trains traveling toward each other on parallel tracks at constant  [#permalink]

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New post 26 Sep 2018, 05:07
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Question Stats:

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Two trains traveling toward each other on parallel tracks at constant rates of 50 miles per hour and 60 miles per hour are 285 miles apart. How far apart will they be 2 hours before their engine meet?

(A) 110
(B) 120
(C) 150
(D) 200
(E) 220
Spoiler: OA

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Two trains traveling toward each other on parallel tracks at constant  [#permalink]

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New post 27 Sep 2018, 04:58
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Bunuel wrote:
Two trains traveling toward each other on parallel tracks at constant rates of 50 miles per hour and 60 miles per hour are 285 miles apart. How far apart will they be 2 hours before their engine meet?

(A) 110
(B) 120
(C) 150
(D) 200
(E) 220


It's a relative speed question.
When they travel toward each other, their relative speed is the sum of the two speeds (50 + 60 = 110 mph)
In 2 hrs, they will together cover a distance of 2*110 = 220 miles.

Hence, 2 hrs before their engines meet, distance between them will be 220 miles.

Answer (E)

Here are some posts on relative speed:
https://www.veritasprep.com/blog/2012/0 ... elatively/
https://www.veritasprep.com/blog/2012/0 ... -concepts/
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Re: Two trains traveling toward each other on parallel tracks at constant  [#permalink]

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New post 27 Sep 2018, 02:57
I am not sure how can we say the gap between two bodies is same as sum of the distance travelled by them.

Maybe I am missing something here.

Requesting you all to give your inputs
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Two trains traveling toward each other on parallel tracks at constant  [#permalink]

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New post 27 Sep 2018, 03:17
Both trains together will take 285/(60+50) hours to meet
i.e. 2 hours 35 mins approx
We need to find how far apart trains will be 2 hours before their engine meet
Therefore, train 1 will be at (50/60*35) miles = 29 miles approx
And Train 2 will be (60/60*35) miles = 35 miles
285 - (29+35) = 221 miles
Answer E which is 220 miles.

I know my approach for solving is not correct.

Can you provide the solution?

Posted from my mobile device
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Re: Two trains traveling toward each other on parallel tracks at constant  [#permalink]

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New post 30 Sep 2018, 13:08
I am not sure i understand. How can sum of speeds define the gap between two moving objects. It tells me how much they have traveled.

The distance here is 285 miles, so the sum of the distance traveled - distance , shouldn't that be distance between them.
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Re: Two trains traveling toward each other on parallel tracks at constant  [#permalink]

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New post 30 Sep 2018, 23:30
Subhrajyoti wrote:
I am not sure i understand. How can sum of speeds define the gap between two moving objects. It tells me how much they have traveled.

The distance here is 285 miles, so the sum of the distance traveled - distance , shouldn't that be distance between them.


There is some gap between them. They travel towards each other for 2 hrs to cover that gap and that is when they meet. Their speeds are fixed at 50 mph and 60 mph.
So in 2 hrs, one of them travels 100 miles and the other travels 120 miles. Together they travel 220 miles in 2 hrs to meet. So the gap between them 2 hrs ago must have been 220 miles.
Say if the gap between them were 330 miles, they would have taken 3 hrs to meet. They would not have met in 2 hrs. 2 hrs happened because the gap between them was 220 miles.
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Re: Two trains traveling toward each other on parallel tracks at constant  [#permalink]

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New post 01 Oct 2018, 00:44
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Bunuel wrote:
Two trains traveling toward each other on parallel tracks at constant rates of 50 miles per hour and 60 miles per hour are 285 miles apart. How far apart will they be 2 hours before their engine meet?

(A) 110
(B) 120
(C) 150
(D) 200
(E) 220


Time it would take for the trains to meet = \(\frac{285}{(50+60)} = 2.59\) hours = \(2\) hours and \(35\) mins (approx.)

Distance between the trains two hours before they meet = \(285\) - Distance travelled by the trains in \(35\) mins = \(285 - \frac{110*35}{60} = 285 - 65\) (approx.) = \(220\) (approx.) Ans E.
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Re: Two trains traveling toward each other on parallel tracks at constant   [#permalink] 01 Oct 2018, 00:44
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