A Mathematical Fairy Tale

“Every day, Jack arrives at the train station from work at 5 pm. His wife picks him up exactly at 5 pm, and drives him home. One day, Jack gets to the station an hour early, and starts walking home, until his wife meets him on the road. They get home 30 minutes earlier than usual. How long was he walking?”

A friend posted this puzzle on our school group. I managed to solve it, not without some difficulty, and to my friend’s great surprise, my answer turned out to be correct.

However, Maths being a bit different from Life, some statements in this puzzle still continue to baffle me.

Every day, Jack arrives at the train station from work at 5 pm.

Firstly, Jack must be a bureaucratic superman if he manages to leave office exactly on time everyday. I suspect he reaches early too and never wastes time gossiping or drinking coffee; grabs a quick bite of lunch between bits of jobs and works with both hands ambidextrously, all the while being aware of a single aim: to catch the train and meet his loving wife at the station at the stroke of five. I don’t know what job the great Jack does, but he must be one hell of an efficient man, for nothing seems to be able to stop him, not piles of files, not angry calls from customers, not last minute requests from superiors.

Secondly, Jack, the quintessential model of virtue, always heads straight for home after work! Not for him, hitting the bar with the boys, nor sneaking out for movies or ball games.

Thirdly, the train arrives, every day, and that too on time. No floods on the tracks, no chain pullers, no strikes, no protesters, no derailments, and no cancellations. Decades ago, once when I reached Pune station well before the departure time of Jhelum Express, I was horrified to see the train leaving the platform. With voluminous baggage plus a wife and a baby, I couldn’t jump into the moving train, so was very upset when the porter carrying my luggage started laughing, till he explained, ‘The one that just left is yesterday’s Jhelum, twenty three hours late! Today’s will be positioned only now that the platform is vacant.’

If Jack were to travel by such a train, wonder what would happen to his wife. She would wilt and wither, waiting without, in wind and weather!

His wife picks him up exactly at 5 pm, and drives him home.

Visualise a humble, obedient wife; who is probably a homemaker or perhaps works part time, and then gives up her afternoon siesta to get ready and pick up her dear hubby from the railway station, every day, without fail, come rain or shine. Crowds don’t delay her, cops don’t stop her and traffic jams always occur after she has passed. She doesn’t go shopping or to the beauty parlour or to her Mom’s place or get busy on the phone with her friends. She never forgets, and, surprise of surprises, she is always on time!

One day, Jack gets to the station an hour early… Which means he left the office an hour early and faithfully headed home. He didn’t hang around the boss’s beautiful secretary or offer to take her out for lunch. No office romances for him nor any platonic walks in the park.

…and starts walking home…  To his own home, without a thought of sneaking away to use this god sent unexpected hour of freedom for some sly business. Really, I would love to have Jack as my son-in-law!

…until his wife meets him on the road.

Now imagine his wife driving diligently, her eyes straight on the road ahead, not eyeing the dresses hanging in the shop windows, not looking at herself in the rear view mirror, not glaring at and judging other women and yet, at the precise moment of their crossing, being able to spot her hardworking husband hurrying home to his loving wife.

They get home 30 minutes earlier than usual. And live happily ever after.


Keeping this mathematical fairy tale aside, in my more realistic mind, this last scene plays out thus:

The wife – let’s call her Jill, just because he is Jack – is driving towards the station. She is looking at everything but the road ahead and slows down as she sees a particularly voluptuous woman wearing less than half of what Jill thinks she should. And then, to her chagrin, she sees Jack chatting with that woman, while they hold hands and laugh.

In the movies, they insert a song at important emotional points in the plot. Since this is a fairy tale, here’s a nursery rhyme playing in the background:

Jack’s wife Jill, went up the hill

To fetch Jack from the station,

Jack she caught, doing what he ought not

And Jill showed her irritation.


Back to angry young Jill, who slams hard on the brakes and does a U turn, throwing the traffic on both sides into disarray. Brakes screech and horns honk and Jack looks up and recognises his wife’s car speeding towards him, and the voluptuous woman, alarmed by the noise, vanishes into the crowd, while Jack stands frozen in fear. Jill parks precisely next to him, without having to move up and down five times like she usually does when parking, and yells, ‘Get in Mister Casanova!’ Jack meekly gets into the car and hurriedly wears his seatbelt as his mad wife dramatically displays her anger by driving dangerously through the traffic. He tries telling her to calm down and slow down, but she does neither and instead screams an unintelligible grunt at the top of her voice, which, to Jack’s husbandly ears, sounds like acoustic terrorism, against which he has no defence and no appeal. He wonders but remains undecided between desiring a quick death in a car accident as against a slow, painful death by his wife’s torturous taunts. Meanwhile, her sight hampered by her fury, Jill loses her way twice, but Jack, usually always quick to point out her navigational errors – politely and lovingly, of course – sits silent and scared and finally, despite having travelled more than the normal distance, thanks to her terrific speed, they get home 30 minutes earlier than usual.

Jill stops the car suddenly, only an inch from the garage door of their beautiful home, turns to Jack, and asks in a cold, steely voice, ‘Who is she?’

‘I don’t know!’ Jack replies, ‘Just a blind girl I helped cross the street.’

And they live occasionally happily ever after!


© Avinash P Chikte


  1. First half of story is based on “Concept of Realities” , but the last half is based on “Physical realities” of a sincere husband, mostly misunderstood by wife!!!. But we all must align with “Physical realities” to avoid being exposed to risks of traffic accident for silly 30 minutes early and help one to cross the road but being married never hold the hand of young lady!!!


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