New York and Boston are 220 miles apart. A train leaves Boston for New York and travels at 65 mph. One hour later, another train leaves New York for Boston and travels at 55 mph. Assume the tracks are straight paths and the trains maintain a constant speed. How far apart are the trains 1 hour before they meet?

As ever, please do NOT post your answers, but do say if you think you have solved the puzzle and how long it took. Solution on Monday.

I have produced an ebook containing 101 of the previous Friday Puzzles! It is called **PUZZLED** and is available for the**Kindle** (UK here and USA here) and on the **iBookstore** (UK here in the USAhere). You can try 101 of the puzzles for free here.

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25 secs to understand what the problem really was, then 2.5 secs to find the solution…. One of the extreme “extremely easy if you just think the right way” puzzles…

Was working it out one way then realised there was a simple answer.

2 mins of thinking about the problem, 5 seconds working out the answer. Like this one🙂

If I had not spent time starting to write down the information while I was reading it, I would have needed no more time than the time needed for the first calculation necessary to solve the problem, since I saw the solution while reading the problem, leaving only the calculation.

About 30 seconds, mainly spent on reading comprehension.

I think I got it in about a minute. Not completely sure I’m right, though.

I started off complicated then i suddenly realised!

Answer came as I was reading it but took another 30 seconds to check there was no twist.

Apperently Dr. wiseman running out of puzzle. It is so easy for me….

Good question is he a dr or prof?

I always assumed you need to be a Dr. to become a Prof.

This one seemed straight-forward, I had an answer as soon ad I’d finished reading it. Hope I haven’t missed something.

This one was really really easy. Took me like 15 secs to read and 5 secs to solve using common sense. Then I took about a minute to solve it algebraically (same answer of course).

“Assume the tracks are straight paths and the trains maintain a constant speed.” And the fields by the track are inhabited by spherical cows.

I am getting so much better at these puzzles. Thank you Richard. 5 seconds on this one.

I can’t believe how much time I spent on writing down and calculating before the answer hit me😉 That’s a very good one!

If I’m right about 15 seconds. I’ve probably missed something. Seems too easy.

doh. nice one.

What about the fly?

My thought exactly.

Also the Fung Wah bus is a lot cheaper than Amtrak

http://www.fungwahbus.com/default.html

the fly realised it had a blue spot on it’s forehead and went into quarantine

@Geoff Coupe: As I started reading the puzzle, I was thinking, “Surely this isn’t going to be about the fly? Richard wouldn’t ask the same puzzle twice!”

Spent a couple of minutes trying to work out the nature of the problem when BAMO the answer was obvious.

Spent ages doing mental algebra for the first time in about twenty-five years, and was pleased when my answer was a nice, round number. Then read the comments saying 5 seconds to solve and went back to the question.

D’oh!

(In my defence, this is my first Friday puzzle, plus my stupidly long method did result in the right answer.)

Not often that I actually realise the solution as I am reading the problem.

About 1 minute wasted on irrelevant considerations and calculations, then about 2 seconds to spot the actual answer.

Solved a set of equations (6min), then reading again saw the solution in the formulation of the question which rendered the equations an unnecessary overkill.😛

But I know how long will it take the trains to meet…

I did the same (and got the bonus answer!) but also drew a graph on a whiteboard. When I looked at the graphic, and the equations, the answer was staring at me.

Had the lightbulb moment about 30 seconds into working it out in my head, then another 2 seconds to do the maths. Enjoyed this one.

Initial mental calculation took 5 secs. However I needed a mathmatical approach to verify my fist assumption. So, another 20 secs to conclude and agree with my first answer.

Simple. 5-10 seconds.

Yes 30 seconds or so reading comprehension a quick sum, then a moment or two looking for twists. Would have actually preferred it if the obvious twist was present.

Does the obvious twist relate to possibility?

The obvious twist would have come into play if he’d asked, “How far apart were the trains one and a half hours before they met?”

One glass of wine too many last night. Goodness me, what was I thinking for so long?

One minute starting to do the sums then 2 seconds to spot the shortcut.

Precisely my experience.

Two reads of the question to understand fully then a (bit of maths) to get the answer. About 30 seconds total.

Too simple – much more interesting to calculate how far it is between the trains at any given time🙂

Or how about the trains accelerating instead of going at constant speed!

30 seconds before the easy answer clicked.

Not the hardest one ever posted.

About 20 sec after reading the last sentence.

Started making complicated calculations, when suddenly after three minutes the simple solution kicked in!

Bonus points for taking into account the curvature of the earth.

Got it with the morning coffee, I started writing things down then realised I didn’t need to.

Like most others I started with paper and pen before reading the whole question and seeing the obvious answer. But there is an additional calculation required to double check that a trick hadn’t been inserted at the start!

Yes – noticed that. Would have made a slightly more interesting question.

Agree, had to check if the cities are far enough apart for the immediate answer to be valid.

it took me 0.033 miles

All in about 2 minutes. Thought it would be more tricky, so set out with my note pad and started to write down the values – then I saw what was going on.

10 seconds to fetch paper and pencil. Then 2 secs to realise I did not need them.

Like many above. About 30 seconds reading, another 30 seconds re-reading to check for tricks.

Then started a complicated calculation which took 2 minutes before realizing the simple method.

The simple method took about 10 seconds. Phew!

Started working it on on paper, only when I reached the end did I realise I only needed to do the last step. Doh!

Like others mention… it is worth doing it the long way, just to test the bounds.

This puzzle reminds me of one for the physics buffs:

If a train travelling at half the light of speed turns on its lights.

What is the perceived speed of light emanating from the train as observed from someone on the ground ?

He he… I was wondering myself if we should correct the answer for relativistic effects.

Speed of light questions still blow the mind. Damn this middle speed, middle sized, world for making our brains stupid.

@Martin: The answer is correct in special relativity, too, as long as we understand that the speeds and distances are relative to a stationary (with respect to New York and Boston) observer. (Ignoring the minor point that, owing to the Earth’s rotation and orbital motion, New York and Boston are always moving relative to each other in any given inertial frame, so we cannot actually have an observer who is stationary with respect to both cities!)

I think it’s interesting the amount of people saying “too easy”, or “would have been better if… ”

But that’s the point here. The solution was designed to be very easy, but the question was designed to trick you into working it out the long way – and in that process, most people _should_ see the obvious solution at the end, although it is still possible to miss that, as even the final calculation can be done backwards.

Well, if you did it the long way, or started to, at least you have this – you now know all kinds of other details of this hypothetical journey.

To some extent, any readers of this blog are going to be expecting a different angle. Why would Dr Wiseman post a straightforward algebra problem? The trick is that there are many possible alternative angles – I was personally testing for the possibility that one of the trains hadn’t left yet.

Like many others I went to fetch pen and paper before realising that the answer was very simple.

Solved while reading.

Pretty much just read it and answered, which is unusual, I think usually I’m slower that most on here.

while the assumption of constant speed is necessary, straight paths are not (a squiggly line is still just a line).

what would make this puzzle more interesting would be if the distance between the two starting points was substantially smaller.

@Chris: That depends on what you mean by “how far apart are the trains”. If you mean how far apart along the track, then the track could be as squiggly as you like and you would get the same answer. But if you mean how far apart as the crow flies (or as the earthworm burrows!), then the shape of the path IS significant.

I quite agree with your second point. If for example the start points were New York and Philadelphia it would take most of us a little longer to work out the answer!

@Nick:

that’s an important observation and you are quite right.

2 mins on a complicated solutions, then realised the simple answer…

A more interesting and trickier question would be if the second train departed 2 hours after the first departed.

peasy easy. the time necessarry for reading the riddle…

then i checked the riddle for any traps just to be sure and fond none.. even considered to calculate the exact positioins of both trains 1 Hour before thy meet..

COME ON!

this is not even a puzzle!

if you come here, find a math puzzle, and try to make calc you know nothing about richard or this page.

Knowing that, the only thing you have to do is think about tricks or twists, and in this puzzle, the very first twist you can imagine is the correct one.

LAME

This was one of my “Oh, God, I’m stupid” moments…

15 seconds. Not really a puzzle imo.

Hehe yeah, I worked it out straight forward with math and all. Then I realised the twist and duh.

Easy and I have 2 answers as well (one of which is a smart alec reply)

I did the math, and then realized the trick. At least I know my algebra still works

Nice,

2 Minutes, After employing mathematics i realize that logic could have been faster. Good one!

I read the puzzle once and thought about it for about 20 seconds. I read the puzzle a second time writing down the values and within 5 seconds I realized the easy solution and had the answer.

Like some, I started working on the math, then realized the answer was simpler than that.

About 10 seconds. But then I’ve seen something similar involving flies.

This is an old, and an easy one. Takes just a few seconds.

One of the easiest.

there is no way of knowing as it depends on the track geometry and train routing. they might be as close as almost touching and still be one hour of track travel apart before they meet.

Had to read the question a couple of times before I got it. Are these getting easier?

this one was fairly easy, but fun easy.

About ten minutes. I figured out how to solve it, then used a paper and pencil for the calculations. As it turned out, if I were better at arithmetic, I probably could have done the whole thing in my head.

Well I had an answer after doing 5mins of maths, then something made me reread the question and I realised that my answer was infact wrong, whilst slapping myself round the head for being so dumb!!

Still now I am feeling confident that I have the right answer and am loking forward to Monday morning.

Richard, if you’re going to criticize the lack of high-speed rail in the US, you may as well be straightforward about it rather than sneaking it into these puzzles.

Great puzzle. Two minutes with 1:58 spent in reading and thinking.

OK smartypants: If the NY bound train left the station at 12:00 noon, what time would it be when the trains are an hour from meeting?

A minute of “This must be simple”, Several minutes trying to calculate stuff, then realising what the actual question was.

8 seconds to get the answer, and about 30 seconds to double-check and re-read and check there wasn’t a nasty twist.

Implausible premise. I live in Connecticut about two blocks from the tracks that these trains would travel upon. They aren’t allowed to go 65 mph in this area. Not to mention the numerous stations they pass by and have to reduce speeds for.😉

Follow up question…

What sort of puzzlers do you get when you’ve reached the bottom of the puzzler barrel?

It took about 1 minute. Hey, I’m getting really fair at this!

Only took me a second.

Though it was the second after I’d worked out they meet 71 miles from New York…

I had the answer before I got to the question. Just like…

I read about a mathematician who was asked a question along these lines – how far does the bee travel…- and he gave an immediate answer. The asker said “Most people try to add up an infinite series.” The math man said, ” That’s what I did!”