To determine how long it will take Stacy to paint the entire room, we can first find her painting rate based on the information provided.
Stacy can paint \( \frac{3}{4} \) of the bedroom in 3 hours. To find the time it takes her to paint the entire bedroom, we can set up a proportion.
Let \( t \) be the time it takes her to paint the entire room.
Since she paints \( \frac{3}{4} \) of the room in 3 hours, we can express the rate of painting as: \[ \frac{\frac{3}{4}}{3 \text{ hours}} = \frac{1}{4} \text{ of the room per hour} \]
Now, to find out how long it takes her to paint the whole room (1 room), we set up the equation: \[ \text{Time} = \frac{\text{Whole room}}{\text{Rate}} = \frac{1 \text{ room}}{\frac{1}{4} \text{ room per hour}} = 4 \text{ hours} \]
So, it will take Stacy \( 4 \) hours to paint the entire bedroom.