Question

sally can paint a room in 8 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? it would take \boxed{} hours. (simplify your answer. type an integer or a fraction.)

Explanation:

Step1: Define work rates

Let the work (painting the room) be 1 unit. Sally's rate: $\frac{1}{8}$ per hour (since she takes 8 hours). Steve's rate: $\frac{1}{6}$ per hour (since he takes 6 hours).

Step2: Combined rate

Combined rate = Sally's rate + Steve's rate = $\frac{1}{8} + \frac{1}{6}$. Find a common denominator (24): $\frac{3}{24} + \frac{4}{24} = \frac{7}{24}$.

Step3: Time to complete work together

Time = Work / Combined rate = $1 \div \frac{7}{24} = \frac{24}{7}$.

Answer:

$\frac{24}{7}$