Answer:
Tuck could use a United States passport to travel because he has the nationality of the United States because he was born in that country. This is so because America guarantees American citizenship to every person born in the national territory, in accordance with the provisions of the Fourteenth Amendment to the United States Constitution.
In addition, Tuck could obtain the citizenship of the United Kingdom, by being her parents of said nation, through the concept of ius sanguinis, by which the nationality is inherited through the descendants.