To answer this problem, let us define that:

x = amount of time Joey can paint a room in hours

1.5 x = amount of time Tina can paint a room in hours

Each person can complete 1 job in the specified amount of

time.

1 job / x hours = rate of Joey

1job / 1.5 x hours = rate of Tina

By adding the two, they can paint the room (1 job) in 6

hours. Therefore:

(1 / x) + (1 / 1.5 x) = 1 / 6

Multiplying whole equation with 6 (x) (1.5 x):

6 (1.5 x) + 6 x = x (1.5 x)

9 x + 6 x = 1.5 x^2

Dividing both sides with x:

15 = 1.5 x

x = 10 hours

Therefore the time it will take Tina, the slower person, is

1.5x = 15 hours

**ANSWER: 15 hours**