2008 AMC 12A Question 10 - thichhoctoan.com

Question 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 $t?$

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