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M03-09

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M03-09  [#permalink]

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New post 16 Sep 2014, 00:19
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Question Stats:

64% (02:09) correct 36% (02:13) wrong based on 268 sessions

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Two trains continuously travel between Washington D.C. and Baltimore which are 120 miles apart. The trains start simultaneously, with train A starting in Washington DC and train B starting in Baltimore, and travel at 30 and 90 mph respectively. If the station turnaround times are negligible, what is the distance between the point where the trains meet for the first time and the point where they meet for the second time?

A. 0
B. 30 miles
C. 60 miles
D. 90 miles
E. 120 miles

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Re M03-09  [#permalink]

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New post 16 Sep 2014, 00:19
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Official Solution:

Two trains continuously travel between Washington D.C. and Baltimore which are 120 miles apart. The trains start simultaneously, with train A starting in Washington DC and train B starting in Baltimore, and travel at 30 and 90 mph respectively. If the station turnaround times are negligible, what is the distance between the point where the trains meet for the first time and the point where they meet for the second time?

A. 0
B. 30 miles
C. 60 miles
D. 90 miles
E. 120 miles


We have train A, which leaves from Washington at the speed of 30 mph and in 1 hour can travel 30 miles. On the other hand, we have the train B that leaves Baltimore at the speed of 90 mph, and, accordingly, can travel 90 miles in 1 hour. As both trains simultaneously leave from the cities to travel the distance of 120 miles, their very first meeting point is 1 hour away from their departure points since train A has traveled 30 miles and train B 90 miles (they traveled 120 miles together). Then train A continues traveling for another hour and now is 60 miles away from Washington. By that time, train B had already reached Washington, had a turnaround and traveled another 60 miles. This is where both trains meet for the second time which is 60 miles away from Washington. The difference between the distances is 60-30=30 miles.


Answer: B
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M03-09  [#permalink]

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New post 13 May 2015, 18:59
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Distance between Washington (W) and Baltimore (B) = 120
Relative speed of trains A and B = 30+90=120
Therefore, the trains together cover a distance of 120 miles in 1 hr and thus meet every hour.

At 1 hr, Train A travels 30 miles from W, Train B travels 90 miles from B. This is where the two trains meet (meeting pt 1).
At 2 hr, Train A reaches 60 miles from W, Train B travels 30 miles to W, turns around in negligible time and reaches 60 miles from W. This is where the two trains meet (meeting pt 2).

Distance between meeting pt 1 and pt2 = 60-30 = 30.

Answer B.

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Re: M03-09  [#permalink]

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New post 03 May 2016, 16:28
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To be pedantic, the distance between Washington, D.C. and Baltimore is actually only about 35 miles.
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Re: M03-09  [#permalink]

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New post 10 Jul 2016, 04:38
:roll: :lol:

PricesWright wrote:
To be pedantic, the distance between Washington, D.C. and Baltimore is actually only about 35 miles.
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Re: M03-09  [#permalink]

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New post 03 Aug 2016, 11:12
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Bunuel wrote:
Two trains continuously travel between Washington D.C. and Baltimore which are 120 miles apart. The trains start simultaneously, with train A starting in Washington DC and train B starting in Baltimore, and travel at 30 and 90 mph respectively. If the station turnaround times are negligible, what is the distance between the point where the trains meet for the first time and the point where they meet for the second time?

A. 0
B. 30 miles
C. 60 miles
D. 90 miles
E. 120 miles



Distance = 120 miles
A's speed : B's speed = 30:90 = 1:3
first meeting point -
A's distance = 1/4 x 120 = 30
B's distance = 3/4 x 120 = 90
So first meeting point is at 30 miles from Washington

At each meeting point, distance by A: distance by B will always be multiple of 1:3
When A=40 B = 120 (not meeting)
When A=50 B = 150 = -30 (not meeting : '-' implies change in direction)
When A =60 B = 180 = -60 (meeting)
So second meeting point is 60 miles from Washington.

Difference between meeting points is 60 -30 =30 miles
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Re: M03-09  [#permalink]

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New post 25 Feb 2018, 02:18
"Again Meeting" somewhat ambiguous. If it were written distance between the point where trains first meet and the point where faster train overtakes, it would be much easier. I calculated the point when trains "again meet" from opposite. And the answer is 60, which is also given.
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Re: M03-09  [#permalink]

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New post 04 May 2019, 23:22
The relative speed of the trains depends on direction - so when both trains are moving in opp directions it is 120mph, while the rel. speed when they move in the same direction is 60mph. so how did you reach the conclusion that they will keep meeting after every 1 hour.
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Re: M03-09   [#permalink] 04 May 2019, 23:22
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