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Math Expert V
Joined: 02 Sep 2009
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Difficulty:   5% (low)

Question Stats: 79% (01:17) correct 21% (01:24) wrong based on 194 sessions

HideShow timer Statistics Train A leaves the Keleti station in Budapest at 5:00PM and travels to Moscow at the speed of 50 mph. If train B leaves Keleti for Moscow some time later on the same day, at what time will train B overtake train A? The distance between the cities is 970 miles.

(1) Train B leaves Keleti at 6:00PM.

(2) Train A travels at $$\frac{5}{6}$$ the speed of train B.

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Math Expert V
Joined: 02 Sep 2009
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Official Solution:

Statement (1) by itself is not sufficient. The speed is also needed to answer the question.

Statement (2) by itself is not sufficient. The departure time is also needed to answer the question.

Statements (1) and (2) combined are sufficient. Approach 1: From S1 we know that train A is already 50 miles ahead of train B. From S2 we can find the speed of train B. $$V_{train B} = \frac{V_{train A}}{\frac{5}{6}} = \frac{50}{\frac{5}{6}} = 60$$mph. Knowing the distance between the trains and the difference between the speed of trains we can find the time when train B overtakes train A. $$\frac{50}{60-50} = 5$$hours. 6PM + 5 hours = 11PM.

Another approach is to use the formula of physics (kinematic): $$x=vt+x_{0}$$ where $$x$$ is the location at time $$t$$ and $$x_{0}$$ is the initial location at time $$t = 0$$

Write the equations of both trains as follows:
$$x_{train A}= 50t + 50$$
$$x_{train B}= 60t$$

$$x_{train A}=x_{train B}$$, represents the time at which the two trains meet each other. Therefore, $$t=5$$ indicates the time difference between the two trains. Add that time to the start of train A to calculate the time at which train B will overtake train A.

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Hey,

Two questions:

- Does this imply that they will meet at 300 miles from Keleti Station as well (since 60*5 = 300)? Maybe at some point before reaching Kiev, one might say... - Is the portion "The distance between the two cities is 970 miles" completely irrelevant to answer this question?

Thanks,
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Math Expert V
Joined: 02 Sep 2009
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minwoswoh wrote:
Hey,

Two questions:

- Does this imply that they will meet at 300 miles from Keleti Station as well (since 60*5 = 300)? Maybe at some point before reaching Kiev, one might say... - Is the portion "The distance between the two cities is 970 miles" completely irrelevant to answer this question?

Thanks,

1. Yes.

2. Not entirely. We need to know that the distance is greater than 300 miles, because if it's not it would need that B won't overtake A while traveling to Moscow.
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I know the GMAT doesn't usually give "gotcha" questions, but I picked E for my answer because this question doesn't mention that the trains are headed in the same direction or on the same tracks. For instance, the train to Moscow could zig-zag east and west, but the Bangalore train could be a straight-shot. Did anyone else determine this question like me?
Intern  B
Joined: 11 Feb 2019
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In this question to arrive at 5 hours later as their intersection point, did we add or subtract the position of Train B (at point 0) from the position of Train A (at point 50) in the formula?
Manager  B
Joined: 18 Jul 2018
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[quote="Bunuel"]Official Solution:

Statement (1) by itself is not sufficient. The speed is also needed to answer the question.

Statement (2) by itself is not sufficient. The departure time is also needed to answer the question.

Statements (1) and (2) combined are sufficient. Approach 1: From S1 we know that train A is already 50 miles ahead of train B. From S2 we can find the speed of train B. $$V_{train B} = \frac{V_{train A}}{\frac{5}{6}} = \frac{50}{\frac{5}{6}} = 60$$mph. Knowing the distance between the trains and the difference between the speed of trains we can find the time when train B overtakes train A. $$\frac{50}{60-50} = 5$$hours. 6PM + 5 hours = 11PM.

Hi Bunuel

Can you please explain the following part again. I couldn't understand it. HOW DID WE CALCULATE 5 hrs ? Why are we using the formula {50/(60-50)}??

"knowing the the distance between the trains and the difference between the speed of trains we can find the time when train B overtakes train A. $$\frac{50}{60-50} = 5$$hours. 6PM + 5 hours = 11PM."

Thanks
Math Expert V
Joined: 02 Sep 2009
Posts: 55804

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JIAA wrote:
Bunuel wrote:
Official Solution:

Statement (1) by itself is not sufficient. The speed is also needed to answer the question.

Statement (2) by itself is not sufficient. The departure time is also needed to answer the question.

Statements (1) and (2) combined are sufficient. Approach 1: From S1 we know that train A is already 50 miles ahead of train B. From S2 we can find the speed of train B. $$V_{train B} = \frac{V_{train A}}{\frac{5}{6}} = \frac{50}{\frac{5}{6}} = 60$$mph. Knowing the distance between the trains and the difference between the speed of trains we can find the time when train B overtakes train A. $$\frac{50}{60-50} = 5$$hours. 6PM + 5 hours = 11PM.

Hi Bunuel

Can you please explain the following part again. I couldn't understand it. HOW DID WE CALCULATE 5 hrs ? Why are we using the formula {50/(60-50)}??

"knowing the the distance between the trains and the difference between the speed of trains we can find the time when train B overtakes train A. $$\frac{50}{60-50} = 5$$hours. 6PM + 5 hours = 11PM."

Thanks

A and B are moving in the same direction. The distance between them is 50 miles. The faster train, which is behind at the time, is moving at 60 miles per hour and slower train is moving at 50 miles per hour. Their relative speed is 60 - 50 = 10 miles per hour (faster train gains 10 miles per hour, so it decreases the distance by 10 miles in one hour). Thus to catch up train A, train B will need 50/10 = 5 hours.

For more on the Relative Speed concept check this: http://www.veritasprep.com/blog/2012/07 ... elatively/

Hope it helps.
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Manager  B
Joined: 18 Jul 2018
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Bunuel wrote:
JIAA wrote:
Bunuel wrote:
Official Solution:

A and B are moving in the same direction. The distance between them is 50 miles. The faster train, which is behind at the time, is moving at 60 miles per hour and slower train is moving at 50 miles per hour. Their relative speed is 60 - 50 = 10 miles per hour (faster train gains 10 miles per hour, so it decreases the distance by 10 miles in one hour). Thus to catch up train A, train B will need 50/10 = 5 hours.

For more on the Relative Speed concept check this: http://www.veritasprep.com/blog/2012/07 ... elatively/

Hope it helps.

THANK YOU Bunuel ! M01-34   [#permalink] 09 Mar 2019, 03:48
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