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

Explanation:

If D can paint the room in 6 hours, in 1 hour she gets
`(1)/(6)` of the room painted;

If C can paint the room in x hours, in 1 hour she gets
`(1)/(x)` of the room painted.

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

`(1)/(6)+(1)/(x)=(1)/(4)` and we need to solve for x. Multiply everything through by the LCM which is 12x:

`12x((1)/(6)+(1)/(x)=(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.