2008 AMC12 A #10

Doug can paint a room in \(5\) hours. Dave can paint the same room in \(7\) hours. Doug and Dave paint the room together and take a one-hour break for lunch. Let \( t\) 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 \(t\)?

(A) \( \left ( \dfrac{1}{5} + \dfrac{1}{7} \right ) (t+1) =1\)

(B) \( \left ( \dfrac{1}{5} + \dfrac{1}{7} \right  ) t +1=1\)

(C) \( \left ( \dfrac{1}{5} + \dfrac{1}{7} \right ) t =1\)

(D) \( \left ( \dfrac{1}{5} + \dfrac{1}{7} \right ) (t-1)=1\)

(E) \( (5+7)t=1\)

정답 (D)