2008 AMC 12A Problems/Problem 10

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Doug can paint $\frac{1}{5}$ of a room per hour. Dave can paint $\frac{1}{7}$ of a room in an hour. The time that they spend working together is $t-1$.

Since rate multiplied by time gives output: $\left(\frac{1}{5}+\frac{1}{7}\right)\left(t-1\right)=1 \Rightarrow D$