Question

one painter can paint a house in 10 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.
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Explanation:

Step1: Define work rates

Let the work (painting the house) be \( W = 1 \). The first painter's rate \( r_1=\frac{W}{t_1}=\frac{1}{10}\) (house per day), the second painter's rate \( r_2 = \frac{1}{3}\) (house per day).

Step2: Combined work rate

When working together, their combined rate \( r = r_1 + r_2=\frac{1}{10}+\frac{1}{3}\). Find a common denominator: \(\frac{3 + 10}{30}=\frac{13}{30}\) (house per day).

Step3: Time to complete work together

Time \( t=\frac{W}{r}=\frac{1}{\frac{13}{30}}=\frac{30}{13}\approx2.308\) days.

Answer:

\( 2.308 \) (or \(\frac{30}{13}\approx2.308\))