Is there any scope for you to agree a 'trial period' for a set amount of time, after which you review whether or not (based on any negative changes in her behaviour/general demeanor/tiredness) to allow her to continue?
There is also a chance of course that the idea of doing 2 extra days may appeal much more to her than the reality when put into practice?
with most teenagers I'd assume "working" meant hanging out with friends but this sounds more organised. I'd let her try, if it gets too much for her deal with it then. Teenagers need to make mistakes sometimes and she will be on a train for hours so getting some rest then.