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

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Train A leaves the station traveling at 30 miles per hour. [#permalink]  09 Feb 2011, 14:16
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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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Re: Train A leaves the station traveling at 30 miles per hour. [#permalink]  09 Feb 2011, 16:03
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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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Re: Train A leaves the station traveling at 30 miles per hour. [#permalink]  09 Feb 2011, 17:56
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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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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Intern Joined: 15 Nov 2014 Posts: 22 Followers: 0 Kudos [?]: 1 [0], given: 27 Re: Train A leaves the station traveling at 30 miles per hour. [#permalink] 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. Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 5555 Location: Pune, India Followers: 1373 Kudos [?]: 6992 [0], given: 179 Re: Train A leaves the station traveling at 30 miles per hour. [#permalink] 03 Mar 2015, 19:59 Expert's post 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 _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Re: Train A leaves the station traveling at 30 miles per hour. [#permalink]  03 Mar 2015, 23:05
Expert's post
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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Re: Train A leaves the station traveling at 30 miles per hour. [#permalink]  04 Mar 2015, 23:55

Refer diagram below:

Attachment:

train.png [ 4.21 KiB | Viewed 916 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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Train A leaves the station traveling at 30 miles per hour. [#permalink]  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]  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]  16 Mar 2015, 20:13
Expert's post
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

[Reveal] Spoiler:
B

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Re: Train A leaves the station traveling at 30 miles per hour.   [#permalink] 16 Mar 2015, 20:13
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