SOLUTION: Working alone, a painter can paint a living room in 6 hours. A second painter can do the job in 9 hours. How long will it take them to paint the room if they work together? Sta

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Question 1027602: Working alone, a painter can paint a living room in 6 hours. A second painter can do the job in 9 hours. How long will it take them to paint the room if they work together? State what x represents, state the equation, and then state the answer.
Answer by ikleyn(54020) About Me  (Show Source):
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Working alone, a painter can paint a living room in 6 hours. A second painter can do the job in 9 hours. How long will it take them to paint the room if they work together? State what x represents, state the equation, and then state the answer.
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Since the first painter can paint a living room in 6 hours, he paints 1%2F6 of the living room area in one hour. It is his rate.

The other painter paints 1%2F9 of the living room area in one hour.

When the two painters work together, they paint 1%2F6+%2B+1%2F9 = 3%2F18+%2B+2%2F18 = 5%2F18 of the room area per hour.

Hence, they need 18%2F5 = 33%2F5 hour = 3 hours and 36 minutes to complete the job, if they work together.


It is typical problem on joint work.

For a variety of similar solved jpint-work problems see the lesson Using fractions to solve word problems on joint work in this site, 
and also associated lessons.