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# While on straight, parallel tracks, train A and train B are traveling

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Math Expert
Joined: 02 Sep 2009
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Kudos [?]: 124574 [0], given: 12079

While on straight, parallel tracks, train A and train B are traveling [#permalink]

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14 Nov 2014, 09:52
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Difficulty:

25% (medium)

Question Stats:

72% (00:59) correct 28% (01:19) wrong based on 200 sessions

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Tough and Tricky questions: Distance/Rate Problems.

While on straight, parallel tracks, train A and train B are traveling at different constant rates. If train A is currently 2 miles behind train B, how many minutes from now will train A be 4 miles behind train B?

(1) Three minutes ago, train A was 1 mile behind train B.

(2) Train A is traveling at 80 miles per hour, and train B is traveling at 100 miles per hour.

Kudos for a correct solution.
[Reveal] Spoiler: OA

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Kudos [?]: 124574 [0], given: 12079

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Re: While on straight, parallel tracks, train A and train B are traveling [#permalink]

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14 Nov 2014, 12:14
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statement 1: sufficient
If 3 minutes ago train A was 1 mile behind and now train A is 2 miles behind, then 3 minutes from now train A will be 3 miles behind and 6 minutes from now train A will be 4 miles behind.

statement 2: sufficient
Train A is 20mph slower than train B. Each hour train A will get 20 miles furthur behind, or 1 mile every 3 minutes.

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Re: While on straight, parallel tracks, train A and train B are traveling [#permalink]

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14 Nov 2014, 19:59
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Statement 1: Three minutes ago, train A was 1 mile behind train B.

To cover 1 extra mile between B and A, it takes 3 mins

Therefore, to cover 2 miles, it would take = 3*2 = 6 mins. Sufficient

Statement 2: Train A is traveling at 80 miles per hour, and train B is traveling at 100 miles per hour.

Relative speed = 20 miles/hr. Let t be the time when the distance between A and B becomes 2 miles.
20 * t = 2
or, t = 2/ 20 hours = 2/20*60 mins = 6 mins. Sufficient

Therefore, D should be the answer

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Re: While on straight, parallel tracks, train A and train B are traveling [#permalink]

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15 Nov 2014, 02:09
1
KUDOS
Statement 1:
From question - Train A is currently 2 miles behind train B
From Statement - Three minutes ago, train A was 1 mile behind train B.

So, to cover 1 mile train takes 3 mins

Therefore, to cover another 2 miles, train will take = 3*2 = 6 mins.
Sufficient. Options B,C,E are out

Statement 2:
Speeds of both the trains are given, so we can calculate relative speed.
Relative speed = 100 - 80 = 20 miles/hr. Now we know both speed and distance so it will be easy to calculate time.
Sufficient
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Re: While on straight, parallel tracks, train A and train B are traveling [#permalink]

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17 Nov 2014, 12:14
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Expert's post
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Bunuel wrote:

Tough and Tricky questions: Distance/Rate Problems.

While on straight, parallel tracks, train A and train B are traveling at different constant rates. If train A is currently 2 miles behind train B, how many minutes from now will train A be 4 miles behind train B?

(1) Three minutes ago, train A was 1 mile behind train B.

(2) Train A is traveling at 80 miles per hour, and train B is traveling at 100 miles per hour.

Kudos for a correct solution.

Official Solution:

While on straight, parallel tracks, train A and train B are traveling at different constant rates. If train A is currently 2 miles behind train B, how many minutes from now will train A be 4 miles behind train B?

We need to know how many minutes, $$t$$, it will take for the distance between train A and train B to increase by 2 miles. The trains are moving at different yet constant speeds, and so the difference between their speeds is also constant. This difference is equivalent to the rate at which train B moves ahead of train A, and since $$\text{distance} = \text{rate} \times \text{time}$$, or $$d=r \times t$$, the distance between the two trains must also change at a constant rate.

Statement 1 says that 3 minutes ago, train A was 1 mile behind train B. Since train A is now 2 miles behind train B, train A must fall behind train B at a rate of 1 mile every 3 minutes. Train A needs to fall behind 2 more miles; that will take $$2 \times 3 = 6$$ minutes. Statement 1 is sufficient to answer the question. Eliminate answer choices B, C, and E. The correct answer choice is either A or D.

Statement 2 gives the rates of both trains. Since the trains' speeds are given in miles per hour, we convert them to miles per minute by dividing them by 60, as there are 60 minutes in an hour. Thus, since train A is going 80 miles per hour, it is going $$\frac{80}{60} = \frac{8}{6} = \frac{4}{3}$$ miles per minute; similarly, train B is going $$\frac{100}{60} = \frac{10}{6} = \frac{5}{3}$$ miles per minute. So, in 3 minutes, train A goes 4 miles and train B goes 5 miles. Thus, train A falls 1 mile farther behind train B every 3 minutes. As we saw in looking at statement 1, this information is enough to answer the question. Statement 2 is also sufficient.

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Re: While on straight, parallel tracks, train A and train B are traveling [#permalink]

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05 Dec 2015, 12:48
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: While on straight, parallel tracks, train A and train B are traveling [#permalink]

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19 Aug 2017, 20:33
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
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Re: While on straight, parallel tracks, train A and train B are traveling   [#permalink] 19 Aug 2017, 20:33
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