To determine how long it will take Stacy to paint the entire room, we first find her painting rate.
Stacy paints \( \frac{3}{4} \) of the bedroom in 3 hours. To find the time it takes to paint the entire room (1 whole room), we can set up the following proportion:
If it takes 3 hours to paint \( \frac{3}{4} \) of the room, let \( x \) be the time it takes to paint the entire room:
\[
\frac{3}{4} \text{ room} \quad \text{in} \quad 3 \text{ hours} = \text{1 room} \quad \text{in} \quad x \text{ hours}
\]
We can establish the equation:
\[
\frac{3/4}{3} = \frac{1}{x}
\]
Cross-multiplying gives us:
\[
3x = 4
\]
Now, solving for \( x \):
\[
x = \frac{4}{3} \times 3 = 4
\]
Now we can confirm it:
To find the time to paint 1 whole room based on the rate:
-
Calculate the amount of room painted per hour:
\[
\text{Rate} = \frac{3/4 \text{ room}}{3 \text{ hours}} = \frac{1}{4} \text{ room/hour}
\]
-
To find out how many hours it takes to paint 1 room:
\[
\text{Time} = \frac{1 \text{ room}}{\text{Rate}} = \frac{1 \text{ room}}{1/4 \text{ room/hour}} = 4 \text{ hours}
\]
Therefore, it will take Stacy 4 hours to paint the entire room.
The correct response is:
4 hours