A group of college students are volunteering for Help the Homeless during their spring break. They are putting the finishing touches on a house they built. Working alone, Irina can paint a certain room in 7 hours. Paulo can paint the same room in 6 hours. Write an equation that can be used to find how long it will take them working together to paint the room. How many hours will it take them to paint the room? If necessary, round your answer to the nearest hundredth.
Let x be the number of hours it takes them to paint the room together. Then, the equation is:
1/7 + 1/6 = 1/x
Multiplying both sides by the least common multiple of 7 and 6, which is 42, we get:
6x + 7x = 42
13x = 42
x = 3.23 (rounded to the nearest hundredth)
Therefore, it will take them about 3.23 hours to paint the room together.