ואתה קח לך מכל מאכל וכו' והיה לך ולהם לאכלה
Why is Noach and his family's food mentioned before the animals' food? The halacha is animals eat before humans.
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The Bnei Yissaschar (R. Tzvi Elimelech of Dinov) explains (in Agra DeKallah on this verse) that since it was a dangerous time [I guess because there was no way to get any other food], then it was proper for the people to eat before the animals, in keeping with the rule that חייך קודמין (your own life takes precedence).
I saw over Shabbos in a Sefer "Peninim M'Shulchan Govoha" that prior to the Mabul it was prohibited to eat meat. The Mitzva of feeding the animals first is mentioned in the Gemara that we learn it from the Posuk in Kriyas Shema "V'Nosati Esev B'Sodicha L'Vhemtecha, V'Ochalto V'Sovoto". Since we were not allowed to eat the meat of animals it was not considered our animals, and therefore prior to the Mabul this Mitzva did not apply.
We shouldn't treat the Ark as we do our regular ships (how on earth did all those animals get inside and live there for a whole year?) but must understand that there are miracles on top of miracles and we are dealing with something very mystical (is this the right word in English?). But anyhow some points for the Shabath table: