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# two trains face each other 100 miles apart on two parallel tracks

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Joined: 28 May 2014
Posts: 475
GMAT 1: 730 Q49 V41
two trains face each other 100 miles apart on two parallel tracks [#permalink]

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03 Nov 2017, 21:28
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Difficulty:

55% (hard)

Question Stats:

65% (01:20) correct 35% (02:03) wrong based on 52 sessions

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two trains face each other 100 miles apart on two parallel tracks. Train B starts moving towards train A at 60 miles/hr. Half an hour later, train A starts moving towards train B at 40 miles/hr. How many miles will train A travel before it passes train B?

(a) 25
(b) 28
(c) 33
(d) 35
(e) 40
[Reveal] Spoiler: OA

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two trains face each other 100 miles apart on two parallel tracks [#permalink]

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03 Nov 2017, 21:42
saswata4s wrote:
two trains face each other 100 miles apart on two parallel tracks. Train B starts moving towards train A at 60 miles/hr. Half an hour later, train A starts moving towards train B at 40 miles/hr. How many miles will train A travel before it passes train B?

(a) 25
(b) 28
(c) 33
(d) 35
(e) 40

What is the main concept used here?

It is the relative speed concepts

s=s1+s2 where s1 and s2 being the speed of train A and train B resp and s is the relative speed.
D= distance between the two trains with both moving.
t=time taken to travel distance D. i.e, time taken for both to meet
Distance traveled by each in that time is given by the ratio of their speed to the relative speed.

we have s= 100
Train B moves alone for 1/2 hour. It would have traveled 30 miles.
So D=100-30=70

Distance traveled by train A=70*(40/100)=28 miles
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two trains face each other 100 miles apart on two parallel tracks [#permalink]

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04 Nov 2017, 10:48
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saswata4s wrote:
two trains face each other 100 miles apart on two parallel tracks. Train B starts moving towards train A at 60 miles/hr. Half an hour later, train A starts moving towards train B at 40 miles/hr. How many miles will train A travel before it passes train B?

(a) 25
(b) 28
(c) 33
(d) 35
(e) 40

Sometimes these questions are called "crash" or "kiss"; distance between is the "gap." A and B move in opposite directions toward one another and will meet.

How far A travels depends on:
-- How far B went alone; and
-- Time for both trains, with both moving, to close the gap

1) Adjust gap distance. B moved alone for a time. Beginning distance = 100 miles

B travels toward A. $$rt=D$$. B covers $$(60mph*\frac{1}{2}hr)= 30$$
miles before A moves. Distance gap is shortened: (100-30) = 70 mi

2) How long to close the gap?

If opposite directions, add rates. Their combined or "relative" rate is (40 + 60) = 100 mph.

Time to close the gap:
$$\frac{Distance}{rate}= time =\frac{70}{100}=\frac{7}{10}hr$$

3) Miles train A will travel before it passes train B? A's travel distance depends only on the shortened gap. So

$$\frac{7}{10} hr * 40mph = 28 miles$$

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two trains face each other 100 miles apart on two parallel tracks   [#permalink] 04 Nov 2017, 10:48
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