If a determined girl worked hard could she be as fit and as strong as a fairly hard working boy? or is it impossible to be as fit and strong as a boy?

Exceptions make rule: Just watch girl Olympic weightlifting competition to get the answer to your question. I would go no where near those women if I thought they might get physical due to any of my action.

Absolutely: Some women are more fit/stronger than men.

Size matters here.: It depends on who you are comparing yourself to. Guys come in different sizes (height and build) and degrees of fitness as well as your own size and body type. It is possible to be more fit and stronger than some, but you will not be as fit or strong as lots of guys because they have more muscle mass and strength generally.