"Are you taking food for three or four days?"
Translation:Berete jídlo na tři nebo čtyři dny?
"Pro" is chiefly used with living beings: e.g. něco pro mě, dárek pro matku, hračka pro psa. It's also used to express agreement, e.g. hlasovat pro něco (vote for something), jsem pro (I agree), and it has a few other specific uses.
Many uses of "for" in English correspond to other prepositions in Czech. E.g.:
Let's go for coffee -> Pojďme na kávu.
You speak a lot of languages, for an American. -> Na Američana umíš hodně jazyků.
A machine for home use -> Stroj na domácí použití
I'm waiting for an answer. -> Čekám na odpověď
I took you for a king. -> Považovala jsem tě za krále.
What do you want for your birthday? -> Co chceš k narozeninám?
He's been living in Prague for 3 years. -> Bydlí v Praze 3 roky. (no preposition)
Berete here means a continuing (ongoing) action. We are taking it with us on this trip and we will have it with us until we use it or return home. It does not always mean repeated action. Vezete is very similar but brát is the direct equivalent of English "take" while the equivalent of "vézt" would be something like "carry".
Do not confuse this usage of "brát" with something like "Berete nějaké léky?" "Do you take any medicine?" That is a different meaning of "take" and of "brát".
"žrádlo" would be acceptable if:
1) you're talking to your dogs (although I don't know how they would be "taking" food)
2) you're asking someone if they're taking food for their pet(s)
3) you're talking to your pals and want to use rough street language
4) you want to be very rude
Number 2 is most likely. Under other circumstances, "žrádlo" is not acceptable for human food.