Stacy is painting her bedroom. She is able to paint 3/4 of the bedroom in 3 hours. At this rate, how long will it take her to paint the entire room?
A: 9/4 hours
B: 12 hours
C: 4 hours
D: 6 hours
If Stacy is able to paint 3/4 of the bedroom in 3 hours, then it takes her 3/(3/4) = 4 hours to paint the entire room.
Thus, the answer is C: 4 hours.
To find out how long it will take Stacy to paint the entire room, we need to calculate the time it takes for one-fourth of the room.
Since she can paint three-fourths of the room in 3 hours, we divide 3 by 3/4.
3 ÷ 3/4 = 3 × 4/3 = 4
Therefore, it will take Stacy 4 hours to paint one-fourth of the room.
Since the entire room consists of four one-fourth sections, it will take her 4 hours × 4 sections = 16 hours to paint the entire room.
The closest option to our answer is B: 12 hours.
To solve this problem, we can set up a proportion.
We know that Stacy can paint 3/4 of the bedroom in 3 hours. Let x be the number of hours it takes her to paint the entire room.
We can set up the proportion: (3/4) / 3 = 1 / x
To solve for x, we can cross-multiply:
(3/4) * x = 3 * 1
Simplifying the equation yields:
3x/4 = 3
Next, we can multiply both sides of the equation by 4/3 to isolate x:
(3x/4) * (4/3) = 3 * (4/3)
The 4/3 on the left-hand side cancels out, leaving us with:
3x = 4
Finally, divide both sides of the equation by 3 to solve for x:
3x / 3 = 4 / 3
x = 4/3
So, Stacy will take 4/3 hours to paint the entire room.
Converting 4/3 to a mixed number, we get:
4/3 = 1 1/3
So, it will take Stacy 1 hour and 1/3 of an hour to paint the entire room.
Since 1/3 of an hour is equal to 20 minutes, Stacy will take 1 hour and 20 minutes to paint the entire room.
Therefore, the answer is not provided among the options given.