How long does it take to recharge a car battery after starting?
No, it isn't Joules in = Joules out. To a first approximation, it's Coulombs in = Coulombs out. It's the electrons flowing through the circuit that participate in the chemical reaction inside the battery (but not at 100% efficiency).

Forget about the energy/power/voltage calculation and just make the ampere-seconds for charging equal to the ampere-seconds for discharging, and then multiply by a fudge factor to account for the inefficiencies.

500A &times; 3s =1500 A-s = 2A &times; 750s = 10A &times; 150s

750s = 12.5 minutes

Figure about 90% efficiency, so the 12.5 minutes / 0.90 = about 14 minutes.