A group of college students is 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 6 hours. Paulo can paint the same room in 9 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, your answer to the nearest, hundredth
Let x be the number of hours it will take Irina and Paulo together to paint the room.
The part of the job each can do in one hour can be written as:
Irina: 1/6
Paulo: 1/9
Together, they complete 1/x of the room in one hour:
1/6 + 1/9 = 1/x
3/18 + 2/18 = 1/x
5/18 = 1/x
Now, to isolate x, we take the reciprocal of both sides:
x = 18/5
x ≈ 3.6
Therefore, it will take Irina and Paulo approximately 3.6 hours to paint the room together.