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Trains


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#21 Zinkyu

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Posted 18 August 2007 - 06:27 PM

Remember, the question isn't about time or speed. Those details are thrown in to throw you off. The question is "When they encounter, which train will be closer?" It's all about position.

So even if they're both at Boston, they will both be the same distance away from New York.
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#22 J2G

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Posted 02 September 2007 - 11:26 AM

You are assuming that the track between New York and Boston is a straight line, and since this is not stipulated, we must assume that the puzzle uses a real train track which exists between New York and Boston. It also doesn't stipulate which country this is in, however, there are no direct trains between New York, UK and Boston, UK the only other country wih both a "New York" and a "Boston" (you need to change trains several times there); therefore again, we must assume that the puzzle is concerned with the rail route between New York - Penn Station, NY and Boston - South Station, MA as serviced by Amtrak - Acela Express whose route is:

Boston - South Station, MA
Boston - Back Bay, MA
Westwood - Route 128 Station, MA
Providence, RI
New London, CT
New Haven, CT
Stamford, CT
New York - Penn Station, NY

For those of you already thinking "Didn't he read the rest of this thread!! i mean honestly... IT DOESN'T MATTER!! Duh!" I will gladly silence your jibber jabber.

Since the track is not a straight line, and consists of at least 2 seperate tracks (one for each direction) along its entire length, there could concievibly be a point along the track that when passing one train is infact closer than the other.

Any idiot who can read a map will tell you that the general direction of a train from Boston to New York is South (if they are more versed in the ways of directional representation, they may say South-West, or better still South-South-West) and it is a distinct possibility that the trian track will weave its way around large obsticles (normally geological) such as hills. if the general direction of the track is south, there maybe a point when the direction of the track actually runs east, or west, or north depending on the obstical it may be avoiding.

Looking at Fig 1 (an illustration only, this may not actually exist!!), you will see clearly that if the trains meet at point A, it will be the south bound train which is closer to New York (think of there being two tracks along the line drawn) but when the track bends east to avoid an obstical, at point B, then it is the North bound train that would be closer to New York. (this is important whether the trains "Pass" or over-lap as someone mentioned, or if they "meet" nose to nose).

Fig 2 shows the basic route, however, it doesn't show all the small twists and turns.

For the answer given by the puzzle setter to be true, then the route would have to be a straight line, which simply is not the case.

NOW.. I have done this rant, someone else can try and work out which train really is closer, even though it will be a matter of meters. (if you want to attempt this you will need: The total length of rail track between the 2 cities note: south bound may be a few meters shorter, the distance between the north bound and south bound tracks, the exact route in at least 1 in 10,000 format, and some kicking algebra skillz.) Good luck.

As an aside (not picking silly holes etc..), i like this puzzle, its a good one.

J2G
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  • bos-ny.gif
  • MAP-LG_acelaexpress.gif

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#23 PMitra

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Posted 03 September 2007 - 12:07 PM

It dosen`t need explanations they will be at same distance from NY...
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#24 JohnSantaFe

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Posted 21 September 2007 - 05:44 PM

The problem with the puzzle is the word encounter. If we take that to mean "when the furthest forward point (nose) of the trains hit each other because the trains are on the same track", then yes the answer is the same distance. However, if the trains are on differnt tracks then there is not enough information as J2G has so thoroughly explained.

Since "they will be at the same distance" is only true for a unique and bizarre case, and "not enough information" holds true for every other case, I'd have to go with the latter.
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#25 IvanOffalich

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Posted 23 September 2007 - 08:18 PM

I'll see if I can explain it for the ones that haven't had the light bulb go off yet:

Assume that the puzzle is asking you which train is closer in miles (or kilometers for our metric friends) to New York.

-It doesn't matter which country the New York and Boston is in and it wouldn't matter if the two cities are Miami, FL and Seattle, WA. It could be any two cities connected by land. Actually, this puzzle could easily substitute planes and any two cities in the world.
-It does not matter which train leaves first and the amount of time of the head start does not matter either.

You may initially think, "Well, it does matter!" assuming that the riddle is about the math. It's not about the math, it's about the logic.

According to Google Maps, New York, NY and Boston, MA are roughly 217 miles apart. Here's why the math doesn't matter (although doing the math can show that math doesn't matter):

Pretend, as one person mentioned, that the train leaving New York with a 5 minute head start could miraculously reach Boston in that 5 minute interval. While it is not possible for a train to travel 217 miles in 5 minutes, it doesn't matter. What matters is that both trains would be 217 miles away from New York.

Now pretend that the trains are traveling slower than most people walk. The first train starts out at a mind blowing 1 mile per hour, the second is traveling at 2 miles an hour... a new land speed record. Doing the math, you'd find that the trains would converge at roughly 73 miles from New York.

You might be saying, "How does that prove that the math doesn't matter?" Well aren't both trains 73 miles from New York at that point? Isn't 73 miles from New York (the distance of the one train) equal to 73 miles from New York (the distance of the other train)?

The point is that no matter what speed the trains go, no matter how much of a head start one train has, the point at which they meet would put the trains at an equal distance in miles/km from New York no matter which point from 0 miles (in New York) to 217 miles (in Boston).

If I met a friend in Chicago, would either of us would be any closer to London (in miles/km) at the time we met? That's really what the question is asking.

Hope this helps,
-Ivan.

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#26 BoilingOil

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Posted 29 September 2007 - 01:59 AM

Ohh, rookie, you almost had me here... It took me a second to realize how redundant this one is. Nice try, really.
Ofcourse, when they encounter, both trains are the same distance from New York. AND from Boston. And, for that matter, from Moskow

BoilingOil
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#27 buzzbuzz

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Posted 05 October 2007 - 04:54 PM

<span style='color:#000000;background:#000000'></span> same distance
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#28 credels

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Posted 16 October 2007 - 10:28 PM

The train leaving NY will be closer to NY until it PASSES the other train. Two things cannot occupy the same space at the same time. Even if train 1 meets train 2 nose to nose, it is still closer to NY...even if it crashes into it. But then, its 1 train?
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#29 GrandmaC

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Posted 23 October 2007 - 03:24 PM

That was just too easy!
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#30 hipowertech

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Posted 01 November 2007 - 11:46 PM

I actually almost hurt my brain on this one (not really)
then I thought once again about the REAL question.....................

When the trains collide,
where will you bury the survivors?


snicker snicker
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