Question

Deandre can paint a small room in 6 hours. Deandre and Casey together can paint the same room in 4 hours. How long would it take for Casey to paint the room alone? Express your answer as a decimal. If necessary, round to the nearest tenth of hour.

Answer 1

Answer:

Step-by-step explanation:

If D can paint the room in 6 hours, in 1 hour she gets $\frac{1}{6}$ of the room painted;

If C can paint the room in x hours, in 1 hour she gets $\frac{1}{x}$ of the room painted.

It takes 4 hours to paint it together. Setting up the classic work equation gives us

$\frac{1}{6}+\frac{1}{x}=\frac{1}{4}$ and we need to solve for x. Multiply everything through by the LCM which is 12x:

$12x(\frac{1}{6}+\frac{1}{x}=\frac{1}{4})$ making our equation simplify to

2x + 12 = 3x and solve for x:

12 = x

C can paint the room alone in 12 hours.