question 1 of 5 type the correct answer in the box. use numerals instead of words. lilly runs a painting…

question 1 of 5 type the correct answer in the box. use numerals instead of words. lilly runs a painting business. she has two experienced interior painters. one painter can paint a 300 - square - foot room in 200 minutes. the other worker can paint a 300 - square - foot room in 300 minutes. if the painters work together, they can paint a 300 - square - foot room in minutes.

question 1 of 5 type the correct answer in the box. use numerals instead of words. lilly runs a painting business. she has two experienced interior painters. one painter can paint a 300 - square - foot room in 200 minutes. the other worker can paint a 300 - square - foot room in 300 minutes. if the painters work together, they can paint a 300 - square - foot room in minutes.

Answer

Explanation:

Step1: Calculate the work - rate of each painter

The first painter can paint a 300 - square - foot room in 200 minutes. So the work - rate of the first painter is $\frac{1}{200}$ rooms per minute. The second painter can paint a 300 - square - foot room in 300 minutes. So the work - rate of the second painter is $\frac{1}{300}$ rooms per minute.

Step2: Calculate the combined work - rate

When they work together, their combined work - rate is the sum of their individual work - rates. So the combined work - rate $r=\frac{1}{200}+\frac{1}{300}$. Find a common denominator, which is 600. Then $\frac{1}{200}+\frac{1}{300}=\frac{3}{600}+\frac{2}{600}=\frac{3 + 2}{600}=\frac{5}{600}=\frac{1}{120}$ rooms per minute.

Step3: Calculate the time taken to paint one room together

We know that work $W = r\times t$. Here, $W = 1$ room and $r=\frac{1}{120}$ rooms per minute. So $t=\frac{W}{r}=\frac{1}{\frac{1}{120}} = 120$ minutes.

Answer:

120