The "many lanes" idea is how Asimov's Expressways solve the problem. The central wide portion (with some subway-car-like seats) moves at 60 mph, with many narrow strips on each side, each 5 mph or so slower than the one inside.For the Sci-Fi-turned-AH file, how about Heinlein's "Rolling roads"? Those were basically giant conveyor belts between cities with passenger compartments and even dining cars on them. They apparently replaced automobiles in his history. I personally think they're totally implausible (for them to be slow enough to step onto reasonably, they'd take forever to get anywhere - unless you have many 'lanes' of varying speed).
The variable-speed detachable cars are used in real life by high-speed ski lifts. A conventional "fixed" lift has to move slowly enough for people to get on and off the moving chairs (around 5 mph max.)- a high-speed lift has a "fast" cable that goes up and down the mountain (at up to 20 mph), and a "slow" cable at each end which is used while people get on and off (at around 2-3 mph).