# A Mathematical Fairy Tale

‘Every day, Jack arrives at the train station from work at 5 pm. His wife picks him up 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 in our school group. I solved it, not without a struggle, and to my friend’s great surprise, my answer turned out to be correct.

Since Maths differs from Life, many statements continue to baffle me.

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

First, Jack must be a bureaucratic superman if he leaves office on the dot daily. 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, always 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’s one hell of an efficient man, for nothing can stop him, not piles of files, not angry calls from customers, not last-minute requests from superiors.

Second, 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.

Third, his train arrives every day by the minute. 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 of Jhelum Express, I watched in horror as I saw it leaving. Having voluminous baggage plus a wife and a baby, I couldn’t jump in, so I shouted in frustration and the porter carrying my luggage started laughing, and he explained, “The one that just left is yesterday’s, twenty-three hours late! Your train will come now.”

If Jack were to travel by such a train, wonder what would happen to his spouse. She might wilt and wither, waiting in wind and weather!

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

Visualise a humble, obedient wife; who is 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 can’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 on the phone with her friends. She never forgets, and, above all, she is never late!

One day, Jack gets to the station an hour early… Which means he left work before time and headed home. He didn’t hang around the boss’s cute secretary or offer to take her for lunch. No office romances for him or 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 opportunity for a clandestine affair.

…until his wife meets him on the road.

Now imagine his partner driving, her eyes straight on the street 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 companion.

They get home 30 minutes earlier than usual.

And live happily ever after.

Wow!

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 watches a voluptuous woman wearing less than half of what Jill thinks she should. And then, to her chagrin, she sees Jack chatting with that shameless slut, while they hold hands and laugh.

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

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.

Angry young Jill slams hard on the brakes and does a U-turn, throwing the traffic on both sides into disarray. Tyres screech and horns honk and Jack looks up and recognises his wife’s car speeding towards him. The voluptuous woman, alarmed by the noise, vanishes into the crowd. Jack stands frozen in fear, while Jill parks right next to him, without her usual clumsiness and yells, “Get in Mister Casanova!”

Jack gets into the car and wears his seatbelt as Jill displays her anger by driving better than a Formula 1 champion through the traffic. He pleads to her to relax and reduce speed, but she does neither. Instead, she screams an unintelligible grunt at the top of her voice. To Jack’s ears, it is acoustic terrorism, against which he has no defence and no appeal.

He remains undecided between desiring a quick demise in a car accident as against a slow, painful death by his wife’s torturous taunts.

Her sight hampered by fury, Jill loses her way twice, but Jack, always quick to point out her navigational errors, sits silent and scared.

Despite travelling more than the normal distance, they reach their residence 30 minutes earlier than usual.

Jill stops the car with a violent jerk, only an inch from the garage door of their elegant dwelling, turns to Jack, and asks in a bitter, 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!

1. Md Anwarul Haque Sardar says:

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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2. Anonymous says:

Wonderful, very well written…

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3. swanandi says:

Very nice, Avinash! Keep it up!

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