It is unclear how old Mr. Burns is. Based on Simpsons canon and various clues throughout the series’ run we can surmise that Charles Montgomery Burns has surpassed the boundaries of human longevity. His vehicle ownership also gives the show’s audience a fair idea that he is from a bygone era:
"You there, fill it up with petroleum distillate and re-vulcanize my tires, post haste. from r/TheSimpsons"
The Ford Quadricycle was the first vehicle developed by Henry Ford and produced from 1896 to 1901. It is a true “Horseless Carriage” that could hit 20 mph under the power of its 59ci two-cylinder 4hp engine. A two-speed manual transmission without reverse was paired with the engine.
In the season seven episode “Scenes From The Class Struggle In Springfield” Mr. Burns drives a Quadracycle to a gas station and says, “You there, fill it up with petroleum distillate and re-vulcanize my tires, post haste.”
Charles Goodyear came up with the concept of vulcanizing tires and received the patent for it in 1844. A part of me thinks that Goodyear and Burns were peers based on using antiquated jargon for tires.
In season nine, episode 20 “The Trouble With Trillions”, Mr. Burns absconds to the airport with Homer and Waylon Smithers. Mr. Burns’ loyal assistant is behind the wheel of his boss’ maroon 1936 Stutz Bearcat.
The Bearcat was introduced in 1912 and was produced until 1924. It was right-hand drive, featured external .gearshift and brake levers, and had a 360ci 16-valve four-cylinder engine. There was a revival of the model in 1931 and its run ended in 1934
At a price of $2,000 in 1914, $52,602 today, it was a luxury vehicle and would suit Mr. Burns. There is the slight issue that there isn’t a 1936 Stutz Bearcat for Mr. Burns to own, but we have suspended reality in regards to his age and we can do the same with the year of his car.
At one time Mr. Burns had a driver’s license issued by the Springfield DMV but it expired in 1909. Even if it hadn’t expired with would been revoked or suspended after he ran over Bart in the show’s second season. The matter went to trial and despite Mr. Burns obvious guilt in the matter the civil suit aspect was doomed by the Simpsons’ lawyer Lionel Hutz. The case was settled for nothing and we don’t see Mr. Burns drive again for four-seasons.
In episode 17 of season seven Mr. Burns operates his own car but it seems that years of being chauffeured about has led him to forget how to drive.
I’m sure the manual will indicate which lever is the velocitator and which the deceleratrix. – Mr. Burns in “Homer the Smithers”.
A cursory search on Merriam-Webster indicates that neither ‘velocitator’ or “deceleratrix” are words. But he conveys his point that he is not clear how ‘modern’ cars operate and his not obeying traffic laws or common sense create havoc in downtown Springfield.
For the greater good of the community maybe it’s better that Smithers drives Mr. Burns around Springfield.