I'm curious why you think it would only take a day of work? Since the only 'specs' are "build a RMI based chat applet" this does leave the door open for many implementations. If I only wanted to send a
string of text to a specific IP address, and didn't care about little details like authenticating users, signing on, managing session state, balancing server chat threads, dealing with dropped connections, monitoring users as they enter/leave, saving chat text, implementing any kind of private messaging feature, etc., etc., etc, I could probably have a "hello world" chat applet done in about a day.
Anything more than this will require much more time.