AMC 12 2012a Problem 13

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

\textbf{(A)}\ 30 \textbf{(B)}\ 36 \textbf{(C)}\ 42 \textbf{(D)}\ 48 \textbf{(E)}\ 60