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 theKindle (UK here and USA here) and on the iBookstore (UK here in the USAhere). You can try 101 of the puzzles for free here.

95 comments

  1. 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.

  2. 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).

    1. @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!”

  3. 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.)

  4. 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…

    1. 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.

  5. 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.

  6. 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.

  7. 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!

  8. 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.

  9. 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!

  10. 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 ?

    1. 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.

    2. @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!)

  11. 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.

  12. 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.

    1. @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.

  13. 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..

  14. 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

  15. 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.

  16. 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.

  17. 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.

  18. 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.

  19. 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?

  20. 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. 😉

  21. 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!”

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