To determine how long it will take Stacy to paint the entire bedroom, we first need to establish her rate of work.
Stacy can paint \( \frac{3}{4} \) of the bedroom in 3 hours. To find the time it takes her to paint the entire room (1 whole room), we can set up the following proportions:
If \( \frac{3}{4} \) of the room takes 3 hours, then 1 whole room takes \( x \) hours:
\[ \frac{3}{4} \text{ of the room} \rightarrow 3 \text{ hours} \] \[ 1 \text{ of the room} \rightarrow x \text{ hours} \]
We can set up the equation:
\[ \frac{3}{4} \text{ room} = 3 \text{ hours} \] \[ 1 \text{ room} = x \text{ hours} \]
To find \( x \), we can create a proportion:
\[ \frac{3}{4} : 3 = 1 : x \]
Cross-multiplying gives us:
\[ 3x = 3 \cdot 4 \]
Solving for \( x \):
\[ 3x = 12 \] \[ x = 4 \]
Thus, it takes 4 hours to paint \( \frac{3}{4} \) of the room, meaning it will take \( x \times \frac{4}{3} = \frac{4}{3} \times 4 = 12 \) hours for the whole room.
So the answer is:
12 hours.