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2008 AMC 10A Problem 13

Problem 13 of 25IntermediateAlgebraArithmetic

Doug can paint a room in 55 hours. Dave can paint the same room in 77 hours. Doug and Dave paint the room together and take a one-hour break for lunch. Let tt be the total time, in hours, required for them to complete the job working together, including lunch. Which of the following equations is satisfied by t?t?

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Solution

Working together, Doug and Dave paint 15+17\dfrac{1}{5} + \dfrac{1}{7} of the room per hour. Because they break for one hour, they work for only t−1t - 1 hours, and this must complete the whole room: (15+17)(t−1)=1. \left(\dfrac{1}{5} + \dfrac{1}{7}\right)(t - 1) = 1. Thus, the correct answer is D.
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