MathDB
Doug + Dave's Painting Team

Source: AMC 12 2008A Problem 10

February 17, 2008
AMC

Problem Statement

Doug can paint a room in 5 5 hours. Dave can paint the same room in 7 7 hours. Doug and Dave paint the room together and take a one-hour break for lunch. Let t 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 t? (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