New York City is a place where attitude and strong opinions are in the DNA. New Yorkers might not agree on much, but there is one thing on which millions of them do agree: the subway is a mess. Trains are packed, breakdowns and delays are routine, some say it's gone off the rails. After an actual derailment last year injured more than 40 people, the governor declared a state of emergency. When it first opened more than a century ago, the New York City subway was considered a feat of American engineering, now it's another example of the country's ailing infrastructure. Luckily, there's a man with a plan, an Englishman in New York who proposes the city's largest infrastructure expenditure since the 1950s. More on that in a moment. First, if you have never ridden the sprawling New York City subway, welcome aboard.

When the trains are moving, there's no better way to get around New York City, than on the subway. These 400-ton behemoths crisscross the underbelly of the city, zipping through a web of tunnels deep underground and on elevated tracks high in the air. Catch one in the right light and it can look like a model train running through a toy cityscape. There's more than 600 miles of track, uptown, downtown, out to the boroughs, like the city itself, the subway never sleeps. It runs 24/7.

Nearly 6 million people ride the trains each day, often accompanied by a soundtrack for the mad dash to the doors.

The cost at the gate? $2.75. For that fare, sometimes you get a show, whether you want it or not. Other times a view. The Empire State Building. There, in the distance, the Statue of Liberty. And here, on the subway, the huddled masses yearning to breathe free.

Ridership is near a 70-year peak, but after years of neglect, deferred maintenance, and financial mismanagement, the system can't handle the strain. Last year, passengers got trapped, desperate on a broken down train for almost an hour in sweltering heat. Earlier this year, a ceiling collapsed on a platform in Brooklyn. One passenger suffered a concussion. In September, torrential rains poured inside a Manhattan station. It all adds up to a mosaic of misery exacerbated by the heat, the rats and incessant delays.

Enter Andy Byford, a world-renowned Mr. Fixit for troubled subways. He's the new president of transit for the Metropolitan Transportation Authority – shorthand, the MTA – the state agency that runs the trains.

Bill Whitaker: This has to be the mother of all transit challenges.

Andy Byford: It is. And the way I look at it, Bill, is someone has to take this on. You know, if every transit professional said, "Oh, it's too tough I'm not gonna risk my career in going there," nothing would happen. I'm prepared to give it a go.

He's certainly got the credentials. Byford grew up a train enthusiast in Britain, in the city of Plymouth. He worked his way up in the London Tube, ran mass transit in Sydney, and most recently led a turnaround in Toronto. The MTA brought him on board in January to stop the hemorrhaging and resurrect the system.

Andy Byford: I pinch myself sometimes 'cause-- how did this spotty kid from Plymouth suddenly end up running New York City Transit? But it's a dream.

Bill Whitaker: Well, some people would call that a nightmare.

Andy Byford: It-- when I left Toronto, there was a mix of people saying congratulations or, "Are you crazy?" But I like a challenge. if we can turn this around, then it'll be the most satisfying period of my career. I mean, it will be the pinnacle.

MTA president Andy Byford surveys one of his stations CBS News

Byford seems undaunted. He proudly wears his nametag for all disgruntled commuters to see, he expects to be held accountable. Like everyone else down here, he just wants the trains to run on time.

Andy Byford: I'm Andy Byford, I'm the president of transit.

With his friendly neighbor approach, he's that rare executive who does his own market research, routinely popping up unannounced to query customers…

Andy Byford: How do you find the service?

Motivate workers…

Andy Byford: Aim high.

WORKER I will…thanks so much.

Andy Byford: Thank you. Thanks for what you do.

And take stock of the subway.

Andy Byford: You know, we got to up our game and get better at the basics.

And if all that glad-handing weren't enough, he also doesn't mind getting those hands dirty.

Bill Whitaker: You really do just pick up----the trash?

Andy Byford: Absolutely. I'm not gonna walk by that.

He's fastidious, down to the last crumb.

Andy Byford: Things like that

Bill Whitaker: Just the trash?

Andy Byford: Yeah, get rid of it. I don't wanna see-- unclean stations or messy stations.

Bill Whitaker: Good luck on that one.

Half-eaten bagels are the least of his worries. Byford was hired to shake up the tired, old system. He crafted a grand modernization plan that calls for hundreds of station renovations, thousands of new subway cars, and more state of the art computer signal controls that can run trains faster and more frequently.

Bill Whitaker: It sounds like you're goin' for broke.

Andy Byford: I've said in the past that's what we have to do. Not to tweak this system. That it needs way more than that. It needs to be a comprehensive, top to bottom modernization of every aspect of our operations. Why shouldn't we be on a par with London, with Hong Kong, with Shanghai, with Singapore? This is New York, for goodness sake.

But the MTA's track record is not world class. Computerizing just one line took about a decade. Byford says, with his planned efficiencies, he can upgrade nearly the entire system in that amount of time. And that would be the easy part. The hard part: how to pay for it. He calculates his plan could cost a whopping $40 billion.

Bill Whitaker: How are you gonna come up with that kinda money?

Andy Byford: Well, I mean, I leave that to smarter people than me. I leave that to the politicians.

But the politicians are squabbling. New York Mayor Bill de Blasio wants to raise money by taxing millionaires. Governor Andrew Cuomo, by charging vehicles squeezing into congested midtown Manhattan. If money and politics weren't enough, Byford says he's going to need a third thing: the patience of New Yorkers who will have to put up with subway lines shutting down for repair.

Bill Whitaker: Any one of those things would be next to impossible to achieve. How are you gonna achieve all three?

Andy Byford: By-- British charm. I'm g-- (LAUGH) It will not be quick. It will not be cheap. And it certainly won't be easy. So my message to New Yorkers is, there's no gain without a bit of pain. This will be worth it.

Tell that to the 400,000 people who take the L train every day, which runs between Brooklyn and Manhattan. The line is facing an imminent, 15-month shutdown for repairs. Riders gave Byford an earful.

The most ambitious element of Byford's plan is ripping out and replacing the antiquated signaling system that controls traffic on the tracks. This is what he inherited: equipment that's been operating since the Great Depression. This machine, more than a hundred years old. We saw operator Rakiya Spady move switches on the tracks around her station by pushing and pulling its antique levers.

Rakiya Spady shows correspondent Bill Whitaker "Old Trusty" CBS News

Bill Whitaker: This is 2018. And this thing was built--

Rakiya Spady: Before we were born. (LAUGH)

Bill Whitaker: Long before. (LAUGH)

Rakiya Spady: Long before. But it --I mean, I call it "Old Trusty." (LAUGH) It's--

Bill Whitaker: "Old Trusty."

Rakiya Spady: --it's movin' the trains.

In this age of GPS, this low-tech map marked the approximate location of nearby trains.

Rakiya Spady: So you see how that green dot is up there behind that blue dot, it's still in transit. So it's moving into the station. And now he's stopped.

Bill Whitaker: But you don't know exactly where on the track that train is.

Rakiya Spady: No.

Bill Whitaker: No.

Bill Whitaker: This is New York City. They don't know exactly where the trains are at any given time in the subway system?

Andy Byford: Yeah, that's what we need to-- transform. It's about accelerating towards a modern signaling system. That would give us precise, absolute identification of where trains are. And it would enable you to move trains up safely, closer together. Ergo, more trains.

The old-fashioned system requires intensive care. When parts break, which at their age happens often, this busy repair shop springs into action. Like doctors, mechanics examine the patients. Some sound like they're on their last breath. Many of the companies that made these components are long gone. So workers here have to manufacture their own replacement parts.

Andy Byford: I have 50,000 employees working with me as a big team. We've got old processes, old systems that we use. And-- and yet, my miracle workers keep that going every day.

Change can't come soon enough for frontline employees like train operators and conductors, who face an increasingly aggravated public. We brought together a small group of veteran workers for what turned into a group therapy session. Melvin Wright is a third-generation train operator.

Melvin Wright: Pulling into a station, people tappin' their watch at me, you know--

Bill Whitaker: Seriously?

Melvin Wright: --remindin' me we're late.

Cheryl Nicholson: That's real-life stuff; that's what goes on.

Cheryl Nicholson is a conductor of 29 years. She says there is no shortage of bad behavior and bad attitudes.

Cheryl Nicholson: I used to really cry.

Bill Whitaker: Because of what people would say to you--

Cheryl Nicholson: Because people were so mean.

And they say it's gotten worse. In August, passengers pummeled a conductor in Brooklyn after the train was forced to skip a few stops. No one here excuses the violence, but we were surprised to hear this.

Cheryl Nicholson: They're frustrated, and I get it.

Bill Whitaker: They have reason to be frustrated?

Cheryl Nicholson: They do have a reason. If your job depends on you to be there and your boss said, you know, this is the third time, Mr. Whitaker. What are you thinking?

Bill Whitaker: I'd say--

Cheryl Nicholson: Oh, that conductor's gonna get it--

Bill Whitaker: It was the MTA.

Cheryl Nicholson: You're causin' me to lose my-- yeah. So--

VOICES: Right, well, yeah--

Cheryl Nicholson: --we get it.

Nothing irritates the traveling public more than delays. On Andy Byford's watch, on-time performance has ticked up slightly, though many riders say they haven't noticed. Byford says he's focused on the basics. He's using $800 million in emergency funds from the state to shift maintenance into overdrive, on the tracks and in the garage, where subway cars are being overhauled at the fastest pace in a decade. Remember Rakia Spady's 100 year old clunker? Her equipment is getting a long-planned upgrade.

Of course, we can't do a story about the subway without hearing from passengers.

To get a quick read on their unvarnished opinions, we went to the MTA's futuristic looking Rail Control Center where workers monitor and manage train-traffic system-wide. There we met Haley Dragoo, a social media millennial who works in:

Haley Dragoo: The Twitter Division.

Bill Whitaker: The Twitter Division?

Haley Dragoo: The Twitter Division.

The Twitter Division gets about 2,000 tweets a day, many from irate passengers.

Haley Dragoo: "What's the purpose of having a schedule if you never abide by it?"

But most of the tweets are from people who just want to know why they can't get to school, work or home on time.

Haley Dragoo: We just kind of try and put ourselves in these people's shoes. And try and answer them as best we can. And as accurately as we can. And then we hope that that made their day a little better or at least more clear.

Bill Whitaker: The subway-riding public is kind of fed up right now.

Andy Byford: And I get that. So our job is crystal clear. We need to turn this around for New Yorkers. And I w-- absolutely want New Yorkers to start feeling, by the end of this year, it's definitely getting better.

Bill Whitaker: By the end of this year?

Andy Byford: By the end of this year.

Wrenching this marvel of the 20th century into the 21st will take a virtuoso performance. New Yorkers are an impatient lot. They want things fixed yesterday. Andy Byford knows he's on the biggest stage, before the toughest crowd on earth.

Bill Whitaker: You've got a lot on your to do list.

Andy Byford: Yeah, one or two things. But that's what I love, it keeps me busy. And the-- the upside is also I get to live in New York. What's not to like?

Produced by Marc Lieberman. Associate producer, Ali Rawaf.