Doug + Dave's Painting Team
Source: AMC 12 2008A Problem 10
February 17, 2008
AMC
Problem Statement
Doug can paint a room in hours. Dave can paint the same room in hours. Doug and Dave paint the room together and take a one-hour break for lunch. Let 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 ?
(A)\ \left(\frac{1}{5}\plus{}\frac{1}{7}\right)(t\plus{}1)\equal{}1 \qquad
(B)\ \left(\frac{1}{5}\plus{}\frac{1}{7}\right)t\plus{}1\equal{}1 \qquad
(C)\ \left(\frac{1}{5}\plus{}\frac{1}{7}\right)t\equal{}1 \\
(D)\ \left(\frac{1}{5}\plus{}\frac{1}{7}\right)(t\minus{}1)\equal{}1 \qquad
(E)\ (5\plus{}7)t\equal{}1