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
