# Tina can paint a room 1.5 times faster than joey can. if they work together, they can paint a room in

###### Question:

## Answers

So, the rate is 1 job / hours, so:

1/n + 1/1.5n = 1/6

We'll make the denominator 3n:

3/3n + 2/3n = 1/6

5/3n = 1/6

Cross multiply:

3n = 30

n = 10

It will take the slower person 10 hours to complete the room.

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