I wanted to add that IF you do decide to accept this arrangement I would NOT bill them solely for the one full time week they do use but would bill them for those 5 days at your part time or even drop in rate.
In other words, if your normal full time weekly rate is say $150 (or $30 per day) I'd bill them at the minimum $200 ($40 per day) if not more. Bottom line is it has to be worth your time.
