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Train Problem

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Frazz: I'm sorry. What was the question again?
Student: Now it's: Why are 40% of story problems and country songs about trains?

The official math problem of TV Land, meant to resemble grade school mathematics problems. "If train A leaves Tropetown at 11:00 towards Idiomopolis that is 32 miles away, moving 50 miles an hour, while train B leaves from Idiomopolis towards Tropetown at 60 miles an hour at 11:30..."


The question is either:

  1. When/if the two trains will reach a certain location,
  2. The number of passengers at time/place Z (where at each station, the movement of people on and off the train is described with bits of math),
  3. Completely irrelevant to the setup details,
  4. Where/when the two trains will meet, in which case, it is almost certainly Denver.

Whatever the intended answer, it's quite likely someone will start asking for entirely irrelevant details.

One variant that pops up occasionally is "which train is closer to City A when they meet?" If the trains have met, they're in the same place, so neither is "closer" to City A. note 

Another variant is to have the question answered in a humorous or joking way, revealing the problem was not mathematical but merely the set-up to a humorous trick-question. Although not train-related, a common example is something like: "One man leaves Tropetown going 80 mph. Another leaves Idiompolis going 75 mph. Where do they meet? IN JAIL! Because the speed limit is 55!"


Often times, vital pieces of information are left out, such as the distance between the cities, or that Train B makes a 20 minute stop in Clicheville. Some irrelevant details may also be added, such as wind speed and direction "to account for wind resistance."note  To show a character is smart they'll come up with these vital missing facts as part of their answer. The most common answer is normally something along the lines of "Who is the idiot that designed this railroad?"

This is (usually) not related to "the Trolley Problem", a philosophical question discussing The Needs of the Many. See also Writers Cannot Do Math, Everybody Hates Mathematics.



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    Anime & Manga 
  • Parodied, like everything else, in Bobobo Bo Bo Bobo.
    Narrator: Pop quiz: If Train A is going 600 miles per hour and Train Bo is going 1,100 kilometers per hour, how long before my head explodes?

    Comic Books 

    Comic Strips 
  • One Far Side strip, titled "Math Phobic's Nightmare", has a man at the gates of the Fluffy Cloud Heaven, with St. Peter asking him this question.
  • Calvin and Hobbes:
    • Calvin's method for answering a question of this sort at school is to turn it into a Film Noir detective mystery in his head. It doesn't quite work, as the answer he comes up with is "a billion". In his defense, Calvin is six, and shouldn't have to tackle that kind of problem anyway.
    • He gets another variant of the problem later, this time with two cars driving down the highway at 5PM. After thinking about the problem for a few seconds, he simply says, "Given the traffic at that hour, who knows?" To be fair, he's not exactly wrong.
  • We get to see it in Frazz here, but then it turns into a country song.
  • FoxTrot did one where Jason listed all the "assumptions" he had to make to give them the answer they wanted (such as the train remaining on the track, not going "as the mole digs", all clocks being accurate, ignoring relativistic effects, etc.)

    Films — Live-Action 
  • In Wayne's World 2, in a vague dream sequence: "Ask me a question", "Ok, if a train leaves a station...", "No, a question about your life"
  • Mentioned during Roman Moronie's trial in the movie Johnny Dangerously.
    Maronie: That's a farging trick question!
  • Used in Deskset with Spencer Tracy and Katherine Hepburn; once seriously, a second time as a joke when they were all a little tipsy during the Christmas Party.
  • The problem is poked fun at with a non-train variant in Sky High (2005) as something of a Funny Background Event. Will is having a quiet, introspective moment while his friends are in the background doing homework.
    Ethan: Your hero flies north at 300 miles per hour for 15 minutes. His archenemy is tunneling south at 200 miles per hour for 10 minutes. Assuming your hero has X-ray vision, how long before he realizes he's going the wrong way?
  • This type of question is in the SAT in The Perfect Score. It's actually plot relevant as reading this question makes Erika become obsessed with who the girl on the train is and where she is going which causes her to not finish the exam.

  • A variation of this problem, using riverboats instead of trains, is faced by Lawrence Pritchard Waterhouse when he joins the navy in Neal Stephenson's Cryptonomicon. He answers with a multi-page dissertation on the problem, attempting to take into account such variables as the speed of the current at different points of the river and the effect it has on the absolute velocity of the vessels. This isn't Obfuscating Stupidity of any kind; a basic train problem is so beneath his genius that it doesn't occur to him that it could challenge anyone, so he honestly assumed that he was supposed to consider the effects of the current on the vessel and the windspeed on its cross-section. He sends a copy of his answer to a mathematics quarterly and gets it published. Meanwhile, the navy has put him in the ship's band because their standardized test has shown he's too dumb to do anything else.
  • The Dodecahedron presents a similar puzzle to Milo, Tock and the Humbug in The Phantom Tollbooth, but one that contains cars, roads, and insufficient information. Tock solves it anyway.
  • One of the Shadowrun short stories in Wolf & Raven starts out with Wolf about to be run down by a car, and feeling like he's trapped in "one of those math problems".
  • A (nonfiction) book parodies of one of these was used to demonstrate how the two hemispheres of your brain work: (paraphrased)
    "Train 1 leaves (City A) towards (City B) at 10:45 and travels at 55 miles per hour, while Train 2 leaves (City B) towards (City A) at 11:15 and travels at 45 miles per hour. How much is the lunch special on the second train?"
  • Dave Barry's Guide to Marriage and/or Sex has this quiz question on "Family Crises," which takes a walking variation and makes the numbers irrelevant to the question:
    Bill and Denise are a young married working couple with no children. One day they set out from Reno, Nevada, on foot at exactly 4:30 P.M. Bill walks three miles per hour and rests for ten minutes each hour, while Denise walks at exactly two miles per hour without stopping. After a couple of days they are both dead from scorpions. Which of the following statements most closely matches your feelings regarding this?
    A. It serves them right.
    B. I hear Reno is quite nice.
    C. I myself prefer a moister climate.
  • The test in The Mysterious Benedict Society features a problem asking how long it will take before two speeding trains collide. Reynie notes in the margin that since the trains are approaching each other on an empty stretch of track, the engineers will likely see each other coming and apply the brakes.

    Live-Action TV 
  • This happened at one point on Dharma & Greg.
  • Sabrina the Teenage Witch also used it, with the added twist that she had to then prevent them from colliding... with her house. (She fails)
  • One of the characters on the The Wire tries to use one of these questions (substituting cars) for his 8th grade math class, but cannot finish the question because the students demand to know what types of cars they are and what neighborhoods they left from.
    • In an earlier season, a juvenile drug runner can't solve a Train Problem, but when it's recast in terms of drug purchases and resupplies, he answers it perfectly. When asked to explain this, he replies, "Count be wrong, they fuck you up."
  • On Saved by the Bell, one of these problems turned up on the SAT.
  • Star Trek: Enterprise "Shuttlepod One" Trip starts rattling off a Train Problem while trying to determine what's wrong with the pod, only to exclaim that he never could work those kind of questions out. Our Chief Engineer, ladies and gentlemen. SF Debris was greatly annoyed at this event. The chief engineer of Earth's most advanced starship can't do one-dimensional algebra.
  • In the episode of NCIS where Abigail Breslin guest stars, a hostage is being held somewhere near railroad tracks and the team's hacked web cam tells them when a train passed her. When they start doing the math to figure out where the train was at that time, Tony admits he'll have to apologize to his high school math teacher, whom he told he would never have to use this problem in Real Life.
  • Mock the Week: "A Virgin train is traveling at 120 miles per hour between London and Manchester, at what time will it be canceled?"
    • "If a train is travelling at 60 miles an hour, how surprised would you be?"
  • In an episode of All in the Family, after a little girl was added to the cast, she is attempting to do a math problem in which a person called A is running at a certain speed, and B is running after them trying to catch up. She asks Archie to help her, only for him to announce that B will never catch A, because "B was chasing A when I was a kid, and if she hasn't caught him by now, she never will."
  • One "Bradley the Big Ol' Baby" sketch from All That provides the most exaggerated use of this trope;
    Miss Fingerly: If a train leaves Japan at 9:22 AMM, heading northeast at 300 MMMPH, and a submarine leaves Nebraska at 8:30 PMM, flying eastwest at 3,000 MMMPH, what time will the two vehicles crash and burn?
  • On My Name Is Earl, in the Creative Writing episode, Joy tells Dodge and Earl Jr. a story to get them to behave themselves and stop whining about having to do homework and pick up their toys. In it, she makes Earl ("Old Daddy") fumble through one of these problems, while (unbeknownst to him) the Crab Shack turns into a desert with train tracks. He gets it wrong, and gets run over by a train, to the kids' horror. Joy explains that that's why she makes them do their homework.
  • The question got brought up in one episode of Due South. Ray admitted that the only answer he could ever come up with was "I don't care".

  • Cirno's Perfect Math Class (and the accompanying Fan Vids) does the "getting on/getting off" version with a bus in Gensokyo. The answer is zero, because there aren't any buses in Gensokyo. Then a train runs over her.

  • Adventures in Odyssey: Connie reads some kids in Whit's End a riddle about an electric train that involves the speed and direction of the train and of the wind. The question is, in which direction is the train's smoke blowing? The answer, of course, is that electric trains don't have any smoke. Connie explodes when the kids don't get it.
  • Often pondered by the navigation officer, Sub-Lieutenant Phillips, on The Navy Lark (among many other things, including references to Noddy's Big Book of Boats). The answer is usually, "Left hand down a bit."

  • Used for a quick pun gag in Children of Eden when the snake first asks two weighty questions of Eve, "If God made all this, who made God?" and "What's beyond the garden?" and then follows it with "If two cranes leave Eden at the same time, and one of them travels at seven times the speed of the other, how long..." before being cut off by Eve.

    Video Games 
  • In Undertale, Mettaton throws one of these at you during his quiz show. Since you have only 30 seconds to read the whole thing and come up with an answer, it's somewhat absurd to expect the player to actually solve it — which might be your cue to notice that Alphys has been sneakily showing you the correct answers with her fingers.

    Visual Novels 
  • Larry Butz of Phoenix Wright: Ace Attorney mentions that he's terrible at these problems when he's trying to change the subject to avoid a question.

    Web Animation 
  • One Homestar Runner sick filler had Homestar subbing in for Strong Bad's "word problem" and using one of these, involving two trains entering a tunnel at four miles per hour.
    Homestar Runner: At what time do they reach Poughkeepsie?

    Web Comics 

    Western Animation 
  • The 2nd episode of The Simpsons, "Bart the Genius," had it as one of the questions on the intelligence test. Complete with Dream Sequence.
  • Done in one episode of Dog City with two protagonists tied up on the bridge that both trains would soon cross.
  • One of the questions used in Darkwing Duck to overload the brain of a super-genius who used a special ray gun to increase his IQ when he had a clear head. DW and Launchpad bombarded him with questions while they fired the ray at him, causing his head to a-splode.
  • In an episode of Clone High dealing with mandatory testing, a Magical Truckdriver gives Gandhi a Train Problem - actually a Trucker and Randy Housewife Problem, asking him to calculate where the two could meet for a "guaranteed" encounter.
  • This was the question that caused Doug to fail a math test.
  • When Oscar Proud decided to help his daughter with her math homework in The Proud Family, this question comes up. He concludes that both trains will meet at the crash site.
  • An episode of The Grim Adventures of Billy & Mandy had a temporary intelligent cat (It Makes Sense in Context...kind of) trying to tutor Billy with a problem like this, but Billy's more worried about what color the train is and who's on it ("Can it be clowns?"), rather than anything relevant to the problem.
  • The Powerpuff Girls once had to face one of these problems in order to figure out where a train collision might occur. As they struggle to find an answer, Blossom delivers a solution: "We're superheroes! Let's just find the two trains and stop them!"
    • Him also gives Blossom this riddle in a Your Worst Nightmare scenario he's conjured for her, as her worst nightmare is failing an upcoming test. The question following the set-up is, "Which train will get to Cuba first?"
      Blossom: Neither — trains don't go to Cuba!
  • In one episode of Big Guy and Rusty the Boy Robot, Rusty ends up fighting an enemy in cyberspace- the Quark building's mainframe, to be precise. In order to buy him some time until Big Guy can be uploaded and help out, Dr. Slate freezes the computers (And the action) by inputting one of these problems into the system. She reveals that that she got kicked out of a computer club for doing that.
  • A question like this came up in a cutaway in the Family Guy Episode, "Mr. Griffin Goes to Washington":
    Gang Member 1: It's three o'clock. Where the hell is Louie?
    Gang Member 2: Well, you tell me. Louie left his house at 2:15 and had to travel a distance of 6.2 miles at a rate of 5 miles per hour. what time will Louie arrive?
    Gang Member 1: Depends if he stops to see his ho.
    Gang Member 2: That's what we call a variable!
  • In the Sonic Boom episode, "The Evil Dr. Orbot", the first question on the test Dr. Eggman takes asks is if a train full of innocent civilians is travelling west at 60 miles per hour and a missile of unspeakable destruction is zooming east at 116 miles per hour, what time the two vehicles will crash and burn. Because Eggman spends so much time trying to answer that one question correctly, he ends up failing the test.
  • In Home: Adventures with Tip & Oh episode "Big Brain Boov", this sort of question is an extra credit on Tip's math homework. Unfortunately, a typo ("why is the train?" instead of "where") causes a Logic Bomb in the literal-minded Boov and nearly causes the collapse of their society.
  • One DC Nation Shazam short has Billy Batson getting this problem at school. Ultimately, he solves the problem by using Shazam's powers to set the trains in motion and see the result. He gets a check minus for not showing his work, however.
  • In the Tiny Toon Adventures episode, "Grandma's Dead", Mrs. Hinkle asks Elmyra one of these, but instead of asking her what time the train would reach the station, she asks how many sandwiches one of the passengers ate.

    Real Life 
  • An anecdote about mathematician John von Neumann has him presented with a variation on this problem: "Two trains start 100 kilometers apart. They head toward each other at 50 kilometers per hour. Meanwhile, a bee flies back and forth between them at 75 kilometers per hour. How far does the bee travel before they collide?" Immediately, von Neumann answered "75 kilometers". The questioner is surprised that he got the answer so quickly, and remarks that most mathematicians solve it by summing an infinite series (representing each stage of the bee's flight) instead of noticing the easy solution (the trains will collide in one hour; therefore the bee flies for one hour; therefore its total flight is 75 kilometers). Von Neumann replied that he did solve it by summing the infinite series.


Video Example(s):

Alternative Title(s): Stock Algebra Puzzle


Doug's Train Problem

A very difficult equation like this causes Doug to flunk a math test... and imagine himself in a train wreck.

How well does it match the trope?

5 (2 votes)

Example of:

Main / TrainProblem

Media sources:

Main / TrainProblem