{"status": "success", "data": {"description_md": "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 $t$?\n\n$\\mathrm{(A)}\\ \\left(\\frac{1}{5}+\\frac{1}{7}\\right)\\left(t+1\\right)=1\\qquad\\mathrm{(B)}\\ \\left(\\frac{1}{5}+\\frac{1}{7}\\right)t+1=1\\qquad\\mathrm{(C)}\\ \\left(\\frac{1}{5}+\\frac{1}{7}\\right)t=1\\mathrm{(D)}\\ \\left(\\frac{1}{5}+\\frac{1}{7}\\right)\\left(t-1\\right)=1\\qquad\\mathrm{(E)}\\ \\left(5+7\\right)t=1$\n___\nFull credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>Doug can paint a room in <span class=\"katex--inline\">5</span> hours. Dave can paint the same room in <span class=\"katex--inline\">7</span> hours. Doug and Dave paint the room together and take a one-hour break for lunch. Let <span class=\"katex--inline\">t</span> 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 <span class=\"katex--inline\">t</span>?</p>&#10;<p><span class=\"katex--inline\">\\mathrm{(A)}\\ \\left(\\frac{1}{5}+\\frac{1}{7}\\right)\\left(t+1\\right)=1\\qquad\\mathrm{(B)}\\ \\left(\\frac{1}{5}+\\frac{1}{7}\\right)t+1=1\\qquad\\mathrm{(C)}\\ \\left(\\frac{1}{5}+\\frac{1}{7}\\right)t=1\\mathrm{(D)}\\ \\left(\\frac{1}{5}+\\frac{1}{7}\\right)\\left(t-1\\right)=1\\qquad\\mathrm{(E)}\\ \\left(5+7\\right)t=1</span></p>&#10;<hr/>&#10;<p>Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 2, "problem_name": "2008 AMC 12A Problem 10", "can_next": true, "can_prev": true, "nxt": "/problem/08_amc12A_p11", "prev": "/problem/08_amc12A_p09"}}