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

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

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

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

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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.

Answer: D.
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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

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

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

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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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