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# Two trains continuously travel between Washington DC and Baltimore

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Manager
Joined: 20 Jun 2016
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Two trains continuously travel between Washington DC and Baltimore  [#permalink]

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09 Aug 2017, 20:16
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Difficulty:

65% (hard)

Question Stats:

61% (02:58) correct 39% (02:43) wrong based on 54 sessions

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Two trains continuously travel between Washington DC and Baltimore, which is 120 miles away. They start simultaneously, train A at Washington and train B at Baltimore, and run at 30 and 90 mph respectively. The station turnaround times are negligible. What is the distance between the point where the trains meet for the first time and the point where they meet for the second time?

0
30 miles
60 miles
90 miles
120 miles

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Re: Two trains continuously travel between Washington DC and Baltimore  [#permalink]

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09 Aug 2017, 20:18
Bunuel please throw some light on this.
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Re: Two trains continuously travel between Washington DC and Baltimore  [#permalink]

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09 Aug 2017, 20:34
30 miles
The first time they meet, it will be in exactly an hour , as train A will have covered 30 miles and train B 90 miles. In total covering complete 120 miles of distance between them. This point will be 30 miles off Washington.
Now in the next our, train A will cover 30 miles towards Baltimore(same direction) and 60miles from Washington. And train B will reach Washington, and turn back and cover 60 additional miles while going back towards Baltimore. So effectively it would also be at 60 miles from Washington , same as train B.
So the first meeting point is 30 miles from Washington, and the next one is 60 miles.
Difference is 30 miles.

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Re: Two trains continuously travel between Washington DC and Baltimore  [#permalink]

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09 Aug 2017, 20:41
Hi Suryangshu,

Given:
The distance between the stations is 120 miles.
Also, train A leaving from W to B is travelling at 30 mph
and train B leaving from B to W is travelling at 90 mph

Relative speed of the trains is 120 mph(since they are travelling in opposite direction)

Hence, they meet for the first time in an hour, as time = distance/speed(relative) = 120/120 = 1
where train A travels 30 miles and train B travels 90 miles. So the point of meeting is 30 miles away from station W.

During the 2nd hour, train A travels another 30 miles towards station W,
and train B after travelling to station W, moves in the direction of station B and will move 60 miles towards it.
They meet again for the second time. This time, however the point of meeting is 60 miles away from station W.

Therefore the distance between the trains meeting for the first time and the second time is 30 miles(Option B)

Hope that helps!
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Re: Two trains continuously travel between Washington DC and Baltimore   [#permalink] 09 Aug 2017, 20:41
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