"Speed Up" is one of the option buttons when a player examines a building or research item that is under construction. If you get friends or allies to help, each one will shorten the construction time by one minute or 1%, whichever is longer. (Until mid-May 2010, it was just "one minute", which was hardly worth the bother for an item taking many hours.)
Get friends to help
Facebook friends will be invited to click a link to help you. Win-win: they get a little prize and you get help.
Get allies to help
A group of items you may have received from Merlin's Magical Boxes will help speed up construction or research.
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