{"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$\\mathrm{(A)}\\ \\left(\\frac{1}{5}+\\frac{1}{7}\\right)\\left(t+1\\right)=1\\qquad\\mathrm{(B)}\\ \\left(\\frac{1}{5}+\\frac{1}{7}\\right)t+1=1\\qquad\\mathrm{(C)}\\ \\left(\\frac{1}{5}+\\frac{1}{7}\\right)t=1\\\\\\mathrm{(D)}\\ \\left(\\frac{1}{5}+\\frac{1}{7}\\right)\\left(t-1\\right)=1\\qquad\\mathrm{(E)}\\ \\left(5+7\\right)t=1$", "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>\n<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>\n<hr><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>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2008 AMC 10A Problem 13", "can_next": true, "can_prev": true, "nxt": "/problem/08_amc10A_p14", "prev": "/problem/08_amc10A_p12"}}