2008 AMC 10A Problem 13

Problem 13 of 25IntermediateAlgebra

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?

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Solution

Working together, Doug and Dave paint

\dfrac{1}{5} + \dfrac{1}{7}

of the room per hour. Because they break for one hour, they work for only

t - 1

hours, and this must complete the whole room:

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

Thus, the correct answer is D.

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