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# Trains

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Trains - Back to the Cool Math Games

A passenger train leaves New York for Boston traveling at the speed of 80 km/hr. In half an hour a freight train leaves Boston for New York traveling at the speed of 60 km/hr.

Which train will be further from New York when they meet?

This old topic is locked since it was answered many times. You can check solution in the Spoiler below.

Pls visit New Puzzles section to see always fresh brain teasers.

Trains - solution

Of course, when the trains encounter, they will be approximately the same distance away from New York. The New York train will be closer to New York by approximately one train length because they're coming from different directions. That is, unless you take "meet" to mean "perfectly overlap".

A train leaves New York for Boston. Five minutes later another train leaves Boston for New York, at double the speed. Which train will be closer to New York when they encounter?

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Posted · Report post

just a bit obvious!

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Im a Moron. I can't believe I sat and did the math on this one before it hit me... LOL

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This is not fair... It totally depends on the distance between the two stations. For people not familiar with these cities and the distance between them it may not be that obvious.

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Im a Moron. I can't believe I sat and did the math on this one before it hit me... LOL

no you're not.. The moron came and posted right after you!!

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Im a Moron. I can't believe I sat and did the math on this one before it hit me... LOL

no you're not.. The moron came and posted right after you!!

zing! xD

that was a good question. i'm stealing it.

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Im a Moron. I can't believe I sat and did the math on this one before it hit me... LOL

no you're not.. The moron came and posted right after you!!

LMAO I didn't even realize what he posted. I love it. Suddenly, I don't feel so stupid anymore...

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Am I the only one who thinks there are missing variables here? or is it my missing knowledge of the geography around NY that is keeping me from solving this problem?

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LMAO

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Am I the only one who thinks there are missing variables here? or is it my missing knowledge of the geography around NY that is keeping me from solving this problem?

I Love it....

Alrighty,,, I'm going to try to explain this one last time... WHY? I don't know, just for the shear fun of seeing how many of you will STILL NOT GET IT....

THE QUESTION IS A SHAM... IT DOES NOT MATTER THE DISTANCE BETWEEN THE POINTS. LOOK AT IT LIKE THIS. LETS SAY YOU ARE AT ONE END OF YOUR STREET, WE WILL CALL YOUR SIDE "SIDE-A" AND I AM AT THE OTHER "SIDE-B". WE ARE BOTH ON BICYCLES. WE START HEADING TOWARD EACHOTHER. ONE IS TRAVELING FASTER THAN THE OTHER, BUT YOU DO NOT KNOW WHICH ONE. "WHEN WE SMACK INTO EACHOTHER, WHO IS CLOSER TO SIDE "A"??? your focusing on the fact that it is impossible to calculate the distance if you do not have more information, which is obvious. It WOULD be impossible to calculate unless you knew how fast they were going, and the distances between the two, HOWEVER......That's not the case....

THE ANSWER IS """""WE ARE AT THE SAME POINT BECAUSE WE JUST SMACKED INTO EACHOTHER""" NEITHER IS CLOSER, WE ARE AT THE SAME POINT. I MEAN, YOU COULD ARGUE IT SAYING THAT THE BACK OF YOUR HEAD IS CLOSER, BUT COME ON... THE POINT IS THAT THE DISTANCE/TIME RATIO DOES NOT MATTER IF THE 2 TRAINS SMACK INTO EACHOTHER. AT THAT POINT, THEY ARE THE SAME DISTANCE FROM BOTH SIDES....

Get it?

I THINK I explained it well,,,, I dunno

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Veracity, you're a little off. The answer to the brain teaser is that the train to New York is closer to New York when it meets the train from Boston. Why? Because things in this world have mass, they aren't points. If everything was points, then yeah, they'd be the same distance from New York when they meet. But think about it, trains are LONG (usually). So that means while the engines of both trains have met, you still have all those cars behind the engine to account for. So obviously, the train coming from New York is still closer to New York.

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Veracity, you're a little off. The answer to the brain teaser is that the train to New York is closer to New York when it meets the train from Boston. Why? Because things in this world have mass, they aren't points. If everything was points, then yeah, they'd be the same distance from New York when they meet. But think about it, trains are LONG (usually). So that means while the engines of both trains have met, you still have all those cars behind the engine to account for. So obviously, the train coming from New York is still closer to New York.

YEP!! Makes sense...LOL

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You know...you really don't have to be so rude about it. I don't know any of you people here. But I think it's something to try to figure out the answers to these logic questions without someone name calling. Why can't you explain things without being so rude?

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You know...you really don't have to be so rude about it. I don't know any of you people here. But I think it's something to try to figure out the answers to these logic questions without someone name calling. Why can't you explain things without being so rude?

I'm not really sure who you are talking about, but if it was me, and I upset you, then I am VERY SORRY!!!.....

Wait,,,,,,

Hold on, I think I,,,,, ()

Ahhhh, There it is......

THE ONLY PERSON BEING RUDE, IS YOU!!! WE ARE JOKING AROUND WITH EACHOTHER WITH ABSOLUTELY NO EMOTION BEHIND ANYTHING WE ARE SAYING. YOU ARE RIGHT, YOU "DO NOT" KNOW ANY OF US YET ARE JUDGING OUR ACTIONS AS IF YOU DO.

We come here everyday and have fun with the Logic puzzles, however it would be quite a boring place without a little Sense of Humor. This is a prime example... You can either read my response and get upset, or TAKE IT WITH A GRAIN OF SALT and tell me TO ATTEND A FEW ANGER MANAGMENT CLASSES...lol..(( I would much rather the Sarcastic "Anger Management comeback myself _))

Are you one of us?

-Veracity-

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Woah...that one almost had me >_< As a side note: Someone should warn those trains, they're both headed toward a serious collision

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Yup, I had the same thought: for point particles this answer works, but for trains with length the one leaving new york is closer unless you define 'encounter' very carefully.

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neither.when they encounter each other they are in the same place.

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I think the answer is so:

the distance from boston and new york isn't important here. Consider that the distance is "x" and consider that both trains are points (because of physics' theory). Using the linear uniform movement equation, you get the following expression:

t1 = x / v (train that leaves new york)

t2 = x / 2v (train that leaves boston)

t1 = time to smack into eachother

t2 = time to smack into eachother

x = distance from new york to boston

As you can see, the faster is the speed the lesser wil be the time to encounter a point that the two trains will smack into eachother. So, if you take a half of time to get the other side of city, probably the two trains will be in the same distance from new york when they encounter eachother.

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This, of course, assumes that there is only one track between New York and Boston. If there were only one track, then yeah I could see the trains smacking into each other.

But yeah, I think I see the point. It's a trick question.

Which train will be closer to New York when they encounter?

When the trains encounter each other, they are technically both the same distance away from Pt. A (because they are on the same point on the line between Pt. A and Pt. B.).

[boston]----------------------------------[wherever the trains have met eachother]---------[New York]

So no matter how fast one train is going versus the other, the distance between the encounter point and New York are the same for both trains (unless you're counting the fact that the train leaving New York has a caboose that's closer to New York than the train leaving Boston).

Does that settle the dispute?

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Well, if the first train takes 5 minutes to get to Boston, they are going to meet in Boston before the other starts going to NY. It totaslly depends on the speed and it is a variable we have to know in order to know the answer.

Otherwise, there are many answers for this question.

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

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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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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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