2012 AMC 12A 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 \qquad\textbf{(B)}\ 36 \qquad\textbf{(C)}\ 42 \qquad\textbf{(D)}\ 48 \qquad\textbf{(E)}\ 60

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.