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 9 hours. Paulo can paint the same room in 8 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 for Irina and Paulo to paint the room together. Then, the equation that relates their individual rates of painting to their combined rate of painting is:
1/9 + 1/8 = 1/x
To solve for x, we can combine the fractions on the left-hand side:
17/72 = 1/x
Multiplying both sides by x, we get:
x = 72/17
Rounding to the nearest hundredth, we get:
x = 4.24 hours
Therefore, it will take Irina and Paulo approximately 4.24 hours working together to paint the room.