Sally can paint a room in 7 hours while it takes Steve 6 hours to paint the same room. How long would it take them to paint the room if they worked together? HW Score: \( 17.65 \%, 3 \) of 17 points It would take \( \square \) hours. (Simplify your answer. Type an integer or a fraction.)

When Sally paints a room, she completes \( \frac{1}{7} \) of the room in one hour, and Steve completes \( \frac{1}{6} \) of the room in one hour. Together, they can complete \( \frac{1}{7} + \frac{1}{6} \) of the room in one hour. To find a common denominator (which is 42), we can rewrite the fractions: \( \frac{1}{7} = \frac{6}{42} \) and \( \frac{1}{6} = \frac{7}{42} \). Adding these gives us \( \frac{6}{42} + \frac{7}{42} = \frac{13}{42} \). This means they can complete \( \frac{13}{42} \) of the room in one hour. To find the total hours to finish one room, we take the reciprocal: \( \frac{42}{13} \) hours, which approximately equals 3.23 hours. So, it would take them \( \frac{42}{13} \) hours or about 3 hours and 16 minutes to paint the room together! By the way, teamwork makes the dream work! When Sally and Steve join forces, their combined effort maximizes efficiency, turning what could be a long day of painting into a fun, collaborative project. Plus, working together means they can split the tasks and maybe even enjoy a few laughs along the way! Also, consider their strategies for mixing paint, setting up the room, and cleaning afterwards. Good planning is essential. They can chat about which area should be painted first or even take turns roller painting and edging – who doesn’t want to show off their skills? Just remember to keep the brushes clean for a smooth finish!