"Mario sits in front of you, you sit behind him," he said. "We didn't get a chance to talk. But, when we got going I was screaming like a little girl, like when you're on a roller coaster."
And, with Hill screaming in the back seat, Andretti clocked more than 180 mph.
So, how did the amateur race-car-driving business for lawyers, insurance brokers, teachers and people like Hill begin?
Bob Lutz, owner of both the Mario Andretti Racing School and the Jeff Gordon Racing School for NASCAR fans, started the Andretti School when he was just 28 years old.
Lutz's father owned short tracks in upstate New York, and from age 8 he spent his summers doing everything from "emptying the garbage to making hot dogs 12 to 16 hours a day" for his dad.
"My father was a great businessman," he said. "I raced go-carts as a kid, but I always knew that I wanted to be involved in the business side of things like him."
At 19, Lutz moved to Charlotte where he met a young aspiring stock-car driver named Jeff Gordon.
"Jeff and I became good friends and then roommates from 1990 to 1993," he said.
While Gordon worked on his racing skills, Lutz founded the Richard Petty Driving Experience, an amateur stock-car-racing school, when he was just 23. The school was a huge success but Lutz sold it four years later after getting "an offer I couldn't refuse" from a faithful customer Leo Hendry, a former CEO of TCI Cable Systems.
"He came to the school about 30 times and I guess he got hooked," Lutz said.
So, a 27-year-old Lutz suddenly found himself retired and with more money he could ever imagine in his bank account, but there was a problem.
He was bored and missed "putting smiles on people's faces," and there was another problem. Lutz had signed a noncompete clause when he sold the Richard Petty Driving School so he couldn't get back into the stock-car business for several years.
His solution was expensive and risky, but paid off enormously for Lutz in the long run.
Only a year after his so-called "retirement," Lutz moved to Las Vegas where he teamed up with a group of engineers and car builders and started the first-ever Indy racing school. At a price tag of $1.2 million to build their first Indy car — Indy cars are more complex than stock cars — it was a costly investment.
But, when superstar racer Mario Andretti signed on to be a part of the business, an overnight hit among dedicated Indy fans was born. Lutz said even today the school was the only place in the world where students could drive full-size Indy cars.
As soon as Lutz's noncompete clause with the new owner of the Richard Petty Driving School had expired, he sped back into the stock-car business as well. Lutz's old roommate Jeff Gordon was, by now, a NASCAR megastar but didn't have a driving school named after him, yet.
So, the Jeff Gordon Racing School for stock-car fans was formed as the sister school to the Mario Andretti Racing School for the Indy fans.
"When I owned the Richard Petty School, we built all the cars in-house," he said, "but, now the NASCAR teams have so many cars — and they cycle through them so fast — that it allows me to use the cars that were driven directly by the pros and buy them when they're done."
Lutz said a typical NASCAR team in the early to mid-1990s would have eight to 12 cars. Today, a team can go through 30 cars in a season.
"If a driver decides he doesn't like some of the cars that are built, I can move in and buy them," said Lutz.
Today, the race-car-school industry for amateur racers, started by the young and eager 23-year-old Bob Lutz, has grown to dozens of racing schools of all kinds that stretch across every corner of the United States. Most are schools that cater to NASCAR fans looking for the excitement of speeding around a track in a stock car like Gordon's.
For Haight, Fernandez and Hill, the thrill of driving an Indy-style race car more than twice the speed limit while hobnobbing with one of the biggest legends in racing was an experience of a lifetime that might seem like a distant dream next time they have a dull day at the office or find themselves standing in line at The Home Depot.