I would probably leave a 13 year old home alone for a short period like that (provided they knew about it in advance and didn't just wake up and find me gone). But I wouldn't leave them in charge of the 6 year old. Or at least, I wouldn't leave my 10 year old, (when she was 13), in charge of a 6 year old. Because I know what she's like. And there's no way she could do the morning routine for her both her and her brother.