In First Contact the Enterprise is sent to patrol the Neutral Zone "in case the Romulans attempt to take advantage of the situation..."

However upon hearing the start of the battle with the Borg they return to Earth at maximum warp.

I've always assumed that the Neutral Zone is a fair distance from Earth... did the battle go on for a long time before the Enterprise arrived (unlikely given the Borg's ability to reduce ships to scrap) or is it actually quite close (relatively)?

How long did it take for the Enterprise to return to Earth?