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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.

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

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14 Nov 2014, 11:14

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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.

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

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14 Nov 2014, 18:59

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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

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

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15 Nov 2014, 01:09

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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 Answer, D _________________

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KUDOS is always a good way to thank anyone. It encourages someone to post more questions and also answers.

KUDOS Please if My post helps you in anyway. Your Kudos keep me alive [/color]

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.

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

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25 Sep 2017, 22:40

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.

Bunuel, I am not sure yet! Where in the question does it indicate whether the two trains are traveling in the same direction or different direction? I read the question again, but I am still not getting any indication about that. In the absence of the direction, I think we can still solve it with option (1), because from option (1) we are getting the rate at which the distance between the two trains is increasing. 1 mile in 3 minutes. So additional 2 miles in additional 6 minutes.

But with option (2), direction is important. If the trains are running at opposite directions, the relative speed becomes 80 + 100 = 180 miles/hr. 180 miles in 60 mins.. so 2 miles in 60/90 = 40 secs.

But if trains are running in same direction, the relative speed is 100 - 80 = 20 miles/hr. 20 miles in 60 mins.... so 2 miles in 6 mins.

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.

Bunuel, I am not sure yet! Where in the question does it indicate whether the two trains are traveling in the same direction or different direction? I read the question again, but I am still not getting any indication about that. In the absence of the direction, I think we can still solve it with option (1), because from option (1) we are getting the rate at which the distance between the two trains is increasing. 1 mile in 3 minutes. So additional 2 miles in additional 6 minutes.

But with option (2), direction is important. If the trains are running at opposite directions, the relative speed becomes 80 + 100 = 180 miles/hr. 180 miles in 60 mins.. so 2 miles in 60/90 = 40 secs.

But if trains are running in same direction, the relative speed is 100 - 80 = 20 miles/hr. 20 miles in 60 mins.... so 2 miles in 6 mins.

I had chosen A as the answer for this question.

We are told that "train A is currently 2 miles behind train B". If the trains are not travelling in the same direction, the word "behind" won't make sense.
_________________

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

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26 Sep 2017, 06:34

Bunuel wrote:

chaudhurysr wrote:

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.

Bunuel, I am not sure yet! Where in the question does it indicate whether the two trains are traveling in the same direction or different direction? I read the question again, but I am still not getting any indication about that. In the absence of the direction, I think we can still solve it with option (1), because from option (1) we are getting the rate at which the distance between the two trains is increasing. 1 mile in 3 minutes. So additional 2 miles in additional 6 minutes.

But with option (2), direction is important. If the trains are running at opposite directions, the relative speed becomes 80 + 100 = 180 miles/hr. 180 miles in 60 mins.. so 2 miles in 60/90 = 40 secs.

But if trains are running in same direction, the relative speed is 100 - 80 = 20 miles/hr. 20 miles in 60 mins.... so 2 miles in 6 mins.

I had chosen A as the answer for this question.

We are told that "train A is currently 2 miles behind train B". If the trains are not travelling in the same direction, the word "behind" won't make sense.

I had thought about that, but then I thought ... even if they are running at opposite directions, train A would still be "behind" train B. Even when we talk about stationary objects, we leave them behind when driving on a road. On the contrary, I honestly thought that was the "trick" part introduced in the question on purpose to test whether test taker catches that or not. In a real GMAT test, should we really assume the direction just based on the interpretation of the word 'behind'? Most of the OG questions I have seen so far, they make directions very clear. GMAT is never shy in using as many words (even extra words) as needed to make sure there is no ambiguity left (e.g. traveling in the same direction, in opposite direction, traveling north, clockwise, anti-clockwise, travels south and then turns around, turns left, turns right etc.). But in this case, I didn't see that. And because this is a DS question, I felt that was the real trap!