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Identical trains A and B are traveling non-stop on parallel tracks fro

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Identical trains A and B are traveling non-stop on parallel tracks fro [#permalink]

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New post 16 Feb 2017, 20:33
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Identical trains A and B are traveling non-stop on parallel tracks from New York to Chicago. Train A leaves New York at 5PM and travels at a constant speed of 55mph (assume constant speed from start of trip). Train B leaves New York at 6:12PM and travels at a constant speed of 66mph (assume constant speed from start of trip). At what time will the two trains be exactly beside each other?

(A) 6:00PM
(B) 7:12PM
(C) 12:00AM
(D) 12:12AM
(E) 1:12AM
[Reveal] Spoiler: OA

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Re: Identical trains A and B are traveling non-stop on parallel tracks fro [#permalink]

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New post 16 Feb 2017, 21:06
Speed of trains
A: 55 mph
B: 66 mph
Rate at which B is reaching towards A= B-A = 11mph

Distance between A and B = 72 mins*55 miles/60 mins

Time taken by B to reach A= 72*55/60/11
=72*55/60*11
= 6 hrs.
So 6.12pm + 6 hrs= 12.12 am.
Option D is the right answer

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Re: Identical trains A and B are traveling non-stop on parallel tracks fro [#permalink]

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hazelnut wrote:
Identical trains A and B are traveling non-stop on parallel tracks from New York to Chicago. Train A leaves New York at 5PM and travels at a constant speed of 55mph (assume constant speed from start of trip). Train B leaves New York at 6:12PM and travels at a constant speed of 66mph (assume constant speed from start of trip). At what time will the two trains be exactly beside each other?

(A) 6:00PM
(B) 7:12PM
(C) 12:00AM
(D) 12:12AM
(E) 1:12AM


By 6:12 Train A would have travelled 66 miles(55 miles in an hr and 11 miles in 12 mins) ahead.

When they meet x*66 = x*55+66;
11x= 66.

Therefore x=6.
so Time would be 6:12+6.
Hence 12:12. Ans:D

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Identical trains A and B are traveling non-stop on parallel tracks fro [#permalink]

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New post 06 Sep 2017, 09:41
hazelnut wrote:
Identical trains A and B are traveling non-stop on parallel tracks from New York to Chicago. Train A leaves New York at 5PM and travels at a constant speed of 55mph (assume constant speed from start of trip). Train B leaves New York at 6:12PM and travels at a constant speed of 66mph (assume constant speed from start of trip). At what time will the two trains be exactly beside each other?

(A) 6:00PM
(B) 7:12PM
(C) 12:00AM
(D) 12:12AM
(E) 1:12AM

Using the gap method in a "chase" scenario.

Train A, while traveling alone, creates the distance (gap) between the trains.

Train A travels alone for \(\frac{6}{5}\) hours * 55 miles/hour = 66 miles

At 6:12 p.m., both trains are moving. But Train B travels faster than train A and will overtake A.

When travelers move in the same direction, subtract slower rate from faster rate to get the rate at which the gap shrinks (relative speed). 66 - 55 = 11 mph

How long will it take for B to catch A? D/r = t. D is 66. r is 11. 66/11 = 6 hours

The clock time at which they are "exactly beside one another" is calculated from the time B leaves, which is when both trains are traveling and the gap begins to shrink.

Add 6 hours to 6:12 p.m. Train B catches Train A at 12:12 a.m.

Answer D

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Re: Identical trains A and B are traveling non-stop on parallel tracks fro [#permalink]

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New post 06 Sep 2017, 11:03
Just one additional thought:

If you wanted to work the problem, it is very easy to remove choices a and b before doing any calculations:

A: 6:00 pm (Train A would have moved for 1.2 hrs at 55 mph while Train B would have made no distance at all)
B: 7:12 pm (Train B would have moved just 1 hr at 66 mph while Train A would have been moving for 2.2 hrs at 55 mph)

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Re: Identical trains A and B are traveling non-stop on parallel tracks fro [#permalink]

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New post 11 Sep 2017, 10:56
hazelnut wrote:
Identical trains A and B are traveling non-stop on parallel tracks from New York to Chicago. Train A leaves New York at 5PM and travels at a constant speed of 55mph (assume constant speed from start of trip). Train B leaves New York at 6:12PM and travels at a constant speed of 66mph (assume constant speed from start of trip). At what time will the two trains be exactly beside each other?

(A) 6:00PM
(B) 7:12PM
(C) 12:00AM
(D) 12:12AM
(E) 1:12AM


We can let the time of train B = t. Train A left 72 minutes earlier than train B, which is 72/60 hours, and thus the time of train A = t + 72/60 = t + 6/5.

Using the formula distance = rate x time, the distance of train A is 55(t + 6/5) = 55t + 66 and distance train B is 66t.

Thus:

distance train A = distance train B

55t + 66 = 66t

66 = 11t

6 = t

So, the trains are besides each other at 6:12 p.m. + 6 hours = 12:12 a.m.

Answer: D
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Re: Identical trains A and B are traveling non-stop on parallel tracks fro   [#permalink] 11 Sep 2017, 10:56
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