As a piano teacher, it depends upon the student and how much practice he/she
puts forth into a piece. I don't know, steponme, how long have you been taking lessons?
It's hard to answer your question here because every student goes at their own pace. There is no set time limit to learn a piece.
I am familiar with the Debussy's Arabesque No. 1, and if you have the
skills and technique to play through it fairly well, then probably a month or so.
Although, the poly-rhythms is always a challenge for anyone to learn, especially for
an intermediate student.