Train A leaves the station traveling at 30 miles per hour. : GMAT Problem Solving (PS)
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Train A leaves the station traveling at 30 miles per hour.

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36. Train A leaves the station traveling at 30 miles per hour. Two hours later train В leaves the same station traveling in the same direction at 40 miles per hour. How far from the station was train A overtaken by train B?
(A) 180
(B) 240
(C) 270
(D) 300
(E) 320
[Reveal] Spoiler: OA
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loveparis wrote:
36. Train A leaves the station traveling at 30 miles per hour. Two hours later train В leaves the same station traveling in the same direction at 40 miles per hour. How far from the station was train A overtaken by train B?
(A) 180
(B) 240
(C) 270
(D) 300
(E) 320


This question tests you on relative speed.
Train A leaves the station traveling at 30 miles/hr. So it covers 30*2 = 60 miles in 2 hrs. After 2 hrs, train B leaves the station. When train B leaves the station, distance between train A and train B is 60 miles since train A has already traveled 60 miles.
Now train B needs to cover up this distance between them by traveling faster than train A. In one hour, train B covers 10 miles more than train A (because train B's speed is 10 miles/hr more than train A's speed). So train B will cover the extra 60 miles in 6 hours.
Train A had traveled for 2 + 6 = 8 hrs before it was overtaken by train B. Hence, it had covered a distance of 8*30 = 240 miles.
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Re: Train A leaves the station traveling at 30 miles per hour. [#permalink]

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Answer = B = 240

Refer diagram below:

Attachment:
train.png
train.png [ 4.21 KiB | Viewed 6549 times ]


Train A has already travelled 60 miles when Train B starts

Say total distance = x from originating point where both trains meet

Time equation would be as follows:

\(\frac{x-60}{30} = \frac{x}{40}\)

x = 240
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When train B catches train A, their location will be the same, and since they left the same point, their distance traveled will be the same.

RT = RT

30mph(T+2) = 40mph(T)

Solve for T. They meet after 6 hours. Plug 6 into either equation and get 240 miles
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New post 03 Mar 2015, 15:00
Hi , Can I know what level of question is that. Is it 600? Thanks.

VeritasPrepKarishma wrote:
loveparis wrote:
36. Train A leaves the station traveling at 30 miles per hour. Two hours later train В leaves the same station traveling in the same direction at 40 miles per hour. How far from the station was train A overtaken by train B?
(A) 180
(B) 240
(C) 270
(D) 300
(E) 320


This question tests you on relative speed.
Train A leaves the station traveling at 30 miles/hr. So it covers 30*2 = 60 miles in 2 hrs. After 2 hrs, train B leaves the station. When train B leaves the station, distance between train A and train B is 60 miles since train A has already traveled 60 miles.
Now train B needs to cover up this distance between them by traveling faster than train A. In one hour, train B covers 10 miles more than train A (because train B's speed is 10 miles/hr more than train A's speed). So train B will cover the extra 60 miles in 6 hours.
Train A had traveled for 2 + 6 = 8 hrs before it was overtaken by train B. Hence, it had covered a distance of 8*30 = 240 miles.
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New post 03 Mar 2015, 19:59
saraafifiahmed wrote:
Hi , Can I know what level of question is that. Is it 600? Thanks.

VeritasPrepKarishma wrote:
loveparis wrote:
36. Train A leaves the station traveling at 30 miles per hour. Two hours later train В leaves the same station traveling in the same direction at 40 miles per hour. How far from the station was train A overtaken by train B?
(A) 180
(B) 240
(C) 270
(D) 300
(E) 320


This question tests you on relative speed.
Train A leaves the station traveling at 30 miles/hr. So it covers 30*2 = 60 miles in 2 hrs. After 2 hrs, train B leaves the station. When train B leaves the station, distance between train A and train B is 60 miles since train A has already traveled 60 miles.
Now train B needs to cover up this distance between them by traveling faster than train A. In one hour, train B covers 10 miles more than train A (because train B's speed is 10 miles/hr more than train A's speed). So train B will cover the extra 60 miles in 6 hours.
Train A had traveled for 2 + 6 = 8 hrs before it was overtaken by train B. Hence, it had covered a distance of 8*30 = 240 miles.


I would say a bit higher - 650-660
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Re: Train A leaves the station traveling at 30 miles per hour. [#permalink]

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New post 03 Mar 2015, 23:05
Hi saraafifiahmed,

This question is a rare version of a "combined rate" question that is sometimes called a "chase down" question (and combined rate questions themselves a rare concept on the GMAT - you'll probably see just one question on it on Test Day). This specific prompt is a relatively easy variation (the speeds, time and answer choices are all round numbers), but the overall concept tends to fall at the higher end of the difficulty spectrum (even though this one is about as easy as the concept gets). You shouldn't worry too much about the difficulty level though - it's not going to be a big point gainer or point loser for you on the Official GMAT (if it shows up at all).

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Train A leaves the station traveling at 30 miles per hour. [#permalink]

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New post 06 Mar 2015, 05:04
Using the RTD chart we get:

..........R........T.........D
A........30.......T............
B........40......T-2..........

So, since we want the distance to be the same, we equate the 2 and find time:

30T = 40 (T-2)
30T = 40T - 80
80 = 10T
T=8

Substituting 8 in the equation for disrance for A we get:
30T = 30*8 = 240.

So, ANS B.
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Re: Train A leaves the station traveling at 30 miles per hour. [#permalink]

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New post 16 Mar 2015, 16:38
Hi all,

Is the following solution/logic correct? Please comment.

Time for which A travels = T + 2
Time for which B travels = T
Relative speed = 10 mph
Distance A travels in 2 hrs = 60 m

Hence, the time in which the gap between A and B "shrinks":

60 = 10 (T+2)
i.e. T = 4 hrs = when A and B meet

In 4 hrs, A traveled 180 m + initial 60 m = 240 m = ANSWER

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Re: Train A leaves the station traveling at 30 miles per hour. [#permalink]

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New post 16 Mar 2015, 20:13
Hi thorinoakenshield,

Yes, your logic is correct - it is a little 'thicker' than it needs to be, but that's okay as long as you're comfortable with the 'steps' involved.

In real basic terms, Train A has a 60 mile "head start" when Train B gets moving. Since the speeds of the two trains are 30mph and 40mph, Train B will "make up" 10 miles every hour.

60 miles = (10mph)(T)
6 hours = T

So, 6 hours after it starts, Train B will catch up to Train A.

(6 hours)(40mph) = 240 miles

Final Answer:
[Reveal] Spoiler:
B


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New post 16 Jul 2015, 23:53
The question: What is the distance from the station where 2 trains meet?

* The speed difference between train A and B is 40 - 30 = 10mph, meaning in every hour,train B covers 10 miles compared to train A.
* In 2 hours train A covers 30mph*2h = 60miles. This is also the distance between 2 trains. Therefore, train B needs to go 60miles/10mph = 6hours to catch up train A.
* In 6 hours, train B goes 40mph * 6hours = 240 miles = where 2 trains meet.
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New post 23 Jul 2015, 07:23
Question: What is the distance where B passes A?

A and B go same direction.
In 2 hours, A go 2h* 30mph = 60 miles.B starts after A goes 2 hours. So the gap between A and B is 60 miles. (1)
B goes faster than A 10mph, meaning in each hour the gap shrinks 10 mile. (2)
From (1) and (2), the total gap = 0 in 60miles/10 miles = 6 hours, meaning B catches A in 6 hours.
Therefore, the distance where A and B meet is 6 hours * 40 mph = 240 miles.
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New post 23 Jul 2015, 22:24
loveparis wrote:
36. Train A leaves the station traveling at 30 miles per hour. Two hours later train В leaves the same station traveling in the same direction at 40 miles per hour. How far from the station was train A overtaken by train B?
(A) 180
(B) 240
(C) 270
(D) 300
(E) 320


Relative Speed = 40 - 30 = 10 Miles per hour
Relative Distance to be overcome = Distance travelled by A in 2 hours before B started = 2*30 = 60 Miles

Time for B to overtake A = Relative Distance / Relative Speed = 60 / 10 = 6 hours

Distance Travelled by B in 6 hours = 40*6 = 240 Miles.

Answer: Option B
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Re: Train A leaves the station traveling at 30 miles per hour.   [#permalink] 09 Sep 2016, 22:09
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