Question

1) Lance can paint the room in 5 hours, while Kim can paint the same room in 4 hours.

Answer 1

1. In an hour, Lance can do 1/5 of the job and Kim can do 1/4 of the same job. Letting x be the number of hours it will take them to do the job together.
                                     (1/5 + 1/4) x = 1
The value of x is 20/9 or approximately 2.22 hours. 

2. Same as the concept above, the equation that would best describe the situation is,
                                   (1/x + 1/2x)(5) = 1
The value of x is 7.5 hours. Since this value is the number of hours Dominique can do the job alone, Houston's time will be 15 hours. 

Answer 2

In 1 hour, Lance can paint $\frac{1}{5}$ of the room.
In 1 hour, Kim can paint $\frac{1}{4}$ of the room.
In 1 hour both will paint;
$\frac{1}{5} + \frac{1}{4}$
$\frac{4}{20} + \frac{5}{20}$
=$\frac{9}{20}$

Together they will take;
$\frac{20}{9}$
=2$\frac{2}{9}$