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Train A leaves New York and is heading towards Boston at a constant

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Train A leaves New York and is heading towards Boston at a constant  [#permalink]

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New post Updated on: 24 Nov 2019, 01:44
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Train A leaves New York and is heading towards Boston at a constant speed, at the same time train B leaves Boston and is traveling to New York in the opposite direction on a parallel track at a constant speed. Train A is traveling faster than train B, and the distance between New York and Boston is 140 miles. When train A reaches Boston, how far is train B from the point at which the two trains passed each other?

(1) Train A is traveling 15 miles per hour faster than train B.
(2) Train B is traveling at a speed that is one-fourth less than that of Train A’s speed.

Source: GMAT Quantum

Originally posted by akash7gupta11 on 23 Nov 2019, 23:51.
Last edited by Bunuel on 24 Nov 2019, 01:44, edited 1 time in total.
Edited the question.
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Re: Train A leaves New York and is heading towards Boston at a constant  [#permalink]

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New post 24 Nov 2019, 00:33
Train A leaves New York and is heading towards Boston at a constant speed, at the same time train B leaves Boston and is traveling to New York in the opposite direction on a parallel track at a constant speed. Train A is traveling faster than train B, and the distance between New York and Boston is
140 miles. When train A reaches Boston, how far is train B from the point at which the two trains passed each other?


We just require the ratio of speed of two or actual speeds of both

(1) Train A is traveling 15 miles per hour faster than train B.
Say B is travelling at 1 and B at 16 and now compare it with A travelling at 115 and B at 100.
Clearly the answers will be different, as A’s speed is way higher than B’s 16 times while the speed in second case is comparable

(2) Train B is traveling at a speed that is one-fourth less than that of Train A’s speed.
Here we know the ratio so we can find the answer.
Suff

B

Now let us find the solution.
So B=3/4 of A.
A:B =4:3 and the distance covered will be in ratio 3:4=60:80..
Now after meeting each other A has to travel 60, so B will travel 3/4 of 60 in that time ..
Answer =60*3/4=45
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Re: Train A leaves New York and is heading towards Boston at a constant  [#permalink]

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New post 24 Nov 2019, 04:54
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chetan2u wrote:
Train A leaves New York and is heading towards Boston at a constant speed, at the same time train B leaves Boston and is traveling to New York in the opposite direction on a parallel track at a constant speed. Train A is traveling faster than train B, and the distance between New York and Boston is
140 miles. When train A reaches Boston, how far is train B from the point at which the two trains passed each other?


We just require the ratio of speed of two or actual speeds of both

(1) Train A is traveling 15 miles per hour faster than train B.
Say B is travelling at 1 and B at 16 and now compare it with A travelling at 115 and B at 100.
Clearly the answers will be different, as A’s speed is way higher than B’s 16 times while the speed in second case is comparable

(2) Train B is traveling at a speed that is one-fourth less than that of Train A’s speed.
Here we know the ratio so we can find the answer.
Suff

B

Now let us find the solution.
So B=3/4 of A.
A:B =4:3 and the distance covered will be in ratio 3:4=60:80..
Now after meeting each other A has to travel 60, so B will travel 3/4 of 60 in that time ..
Answer =60*3/4=45

sir isnt there a formula giving the same :could you please help to enumerate that
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Re: Train A leaves New York and is heading towards Boston at a constant  [#permalink]

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New post 24 Nov 2019, 10:41
akash7gupta11 wrote:
Train A leaves New York and is heading towards Boston at a constant speed, at the same time train B leaves Boston and is traveling to New York in the opposite direction on a parallel track at a constant speed. Train A is traveling faster than train B, and the distance between New York and Boston is 140 miles. When train A reaches Boston, how far is train B from the point at which the two trains passed each other?

(1) Train A is traveling 15 miles per hour faster than train B.
(2) Train B is traveling at a speed that is one-fourth less than that of Train A’s speed.

Source: GMAT Quantum


Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
Visit https://www.mathrevolution.com/gmat/lesson for details.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify conditions if necessary.

Assume \(v_a\) and \(v_b\) are speeds of the train A and B, respectively, and \(t\) is the time the train takes to reaches Boston.
Then \(v_a \cdot t = 140\).
And the question asks the value of \(140 - v_b \cdot t = v_a \cdot t - v_b \cdot t = (v_a - v_b)t\).


Since we have \(v_b = \frac{1}{4}v_b\) from condition 2).
\(v_b \cdot t = \frac{1}{4} v_a \cdot t = \frac{140}{4} = 35\).
\(140 - v_b \cdot t = 140 - 35 = 105\).
Condition 2) is sufficient.

Condition 1)
We have \(v_a - v_b = 15\) from condition 1), but we don't any information about \(t\).
We can't determine the value of \(140 - v_b \cdot t = v_a \cdot t - v_b \cdot t = (v_a - v_b)t = 15t\).

Since condition 1) does not yield a unique solution, it is not sufficient.

Therefore, B is the answer.
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Re: Train A leaves New York and is heading towards Boston at a constant   [#permalink] 24 Nov 2019, 10:41
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