# Problem #1688

 1688 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? $\textbf{(A)}\ 30 \qquad\textbf{(B)}\ 36 \qquad\textbf{(C)}\ 42 \qquad\textbf{(D)}\ 48 \qquad\textbf{(E)}\ 60$ This problem is copyrighted by the American Mathematics Competitions.
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• Reduce fractions to lowest terms and enter in the form 7/9.
• Numbers involving pi should be written as 7pi or 7pi/3 as appropriate.
• Square roots should be written as sqrt(3), 5sqrt(5), sqrt(3)/2, or 7sqrt(2)/3 as appropriate.
• Exponents should be entered in the form 10^10.
• If the problem is multiple choice, enter the appropriate (capital) letter.
• Enter points with parentheses, like so: (4,5)
• Complex numbers should be entered in rectangular form unless otherwise specified, like so: 3+4i. If there is no real component, enter only the imaginary component (i.e. 2i, NOT 0+2i).