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)