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A 350uf supercap bank capable of starting a 4 cyl car has a capacity of around 200mah, you can charge it in seconds, but not with a standard 12v car charger, a large jump starter pack would be the way to go (just because caps will suck a lot of current). That's roughly the same total capacity as two 9V smoke alarm batteries, so you don't need a big back up battery if you keep currents in check.
On the Suzuki Swift I got four starts back to back from mine before the caps were too weak to crank it.
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