Question

module 7 pretest: rational expressions and equations
score: 7/9 answered: 7/9
question 8
one painter can paint a house in 9 days, yet a more experienced painter can paint the house in 3 days. how many days would it take the two painters, working together, to paint the house?
it will take them days to paint the house together.
if needed, round answer to 3 decimal places.

Explanation:

Step1: Define work rates

Let the first painter's rate be \( r_1=\frac{1}{9} \) (houses per day), and the experienced painter's rate be \( r_2=\frac{1}{3} \) (houses per day). The combined rate \( r = r_1 + r_2 \).

Step2: Calculate combined rate

\( r=\frac{1}{9}+\frac{1}{3}=\frac{1 + 3}{9}=\frac{4}{9} \) (houses per day).

Step3: Find time for combined work

Time \( t \) is reciprocal of rate: \( t=\frac{1}{r}=\frac{9}{4} = 2.25 \) days.

Answer:

2.25