Paula the painter and her two helpers each paint at constant, but different, rates. They always start at $8:00 \text{ AM}$, and all three always take the same amount of time to eat lunch. On Monday, the three of them painted $50\%$ of a house, quitting at $4:00 \text{ PM}$. On Tuesday, when Paula wasn't there, the two helpers painted only $24\%$ of the house and quit at $2:12 \text{ PM}$. On Wednesday, Paula worked by herself and finished the house by working until $7:12 \text{ PM}$. How long, in minutes, was each day's lunch break?

Let's think step by step and output the final answer within \boxed{}.
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