Electric current is a very slow flow of charges, while
energy flows fast
I'm not sure where you got it. Electric current is a flow of charge. Charge
moves in the wire in speed close to speed of light. It has nothing to do with
slow motion of electrons and charges they carry. It works pretty much as
stack of balls (electric charges) - you hit first one and the last one moves
instantly.
http://www.uu.edu/dept/physics/scienceguys/2001Nov.cfm