Answer
The influence of one electron on another propagates through the wire at nearly the speed of light, causing almost instant movement of all electrons in the wire.
Work Step by Step
The electrons move with a rather slow average speed along the wire, (a hundredth of a centimeter per second), but the influence they have on one another, due to the electrostatic force, moves through the wire at nearly the speed of light.
This propagating influence causes almost instant movement of all electrons in the wire. When electrons move, current is produced.
