If Stacy can paint \( \frac{3}{4} \) of the bedroom in 3 hours, we can first determine how long it takes her to paint the entire bedroom by finding the time per fraction of the room she paints.
To find the time it takes to paint the entire room, we can set up a proportion based on the information provided.
If \( 3 \) hours is required to paint \( \frac{3}{4} \) of the room, the time \( T \) to paint the whole room can be calculated as follows:
\[ T = \left( \text{Total Room} \right) \div \left( \text{Part of Room per Time} \right) \]
The total room is \( 1 \) (whole room), and the part of the room painted in 3 hours is \( \frac{3}{4} \):
\[ T = 3 , \text{hours} \div \left( \frac{3}{4} , \text{of a room in 3 hours} \right) \]
To find the entire room's time, we can multiply 3 hours by the reciprocal of \( \frac{3}{4} \):
\[ T = 3 \times \left( \frac{4}{3} \right) = 4 , \text{hours} \]
Thus, it will take her 4 hours to paint the entire room.