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, round your answer to the nearest hundredth(1 point)%0D%0AResponses%0D%0A%0D%0Ax8+x7=1; 3.73 hours%0D%0A%0D%0A8%0D%0A+%0D%0A%0D%0A7%0D%0A=%0D%0A1%0D%0A;%0D%0A %0D%0A3.73%0D%0A %0D%0Aℎ%0D%0A%0D%0A%0D%0A%0D%0A%0D%0Ax8+x7=1; 3.73 hours%0D%0A%0D%0A8%0D%0A+%0D%0A%0D%0A7%0D%0A=%0D%0A1%0D%0A;%0D%0A %0D%0A3.73%0D%0A %0D%0Aℎ%0D%0A%0D%0A%0D%0A%0D%0A%0D%0A%0D%0A6+92; 7.5 hours%0D%0A6%0D%0A+%0D%0A9%0D%0A2%0D%0A;%0D%0A %0D%0A7.5%0D%0A %0D%0Aℎ%0D%0A%0D%0A%0D%0A%0D%0A%0D%0A6+92; 7.5 hours%0D%0A6%0D%0A+%0D%0A9%0D%0A2%0D%0A;%0D%0A %0D%0A7.5%0D%0A %0D%0Aℎ%0D%0A%0D%0A%0D%0A%0D%0A%0D%0A%0D%0Ax6+x9=1; 3.6 hours%0D%0A%0D%0A6%0D%0A+%0D%0A%0D%0A9%0D%0A=%0D%0A1%0D%0A;%0D%0A %0D%0A3.6%0D%0A %0D%0Aℎ%0D%0A%0D%0A%0D%0A%0D%0A%0D%0Ax6+x9=1; 3.6 hours%0D%0A%0D%0A6%0D%0A+%0D%0A%0D%0A9%0D%0A=%0D%0A1%0D%0A;%0D%0A %0D%0A3.6%0D%0A %0D%0Aℎ%0D%0A%0D%0A%0D%0A%0D%0A%0D%0A%0D%0A6x+9x=1; 15 hours
To find how long it will take Irina and Paulo to paint the room together, we can use the equation:
1/6 + 1/9 = 1/x
Simplifying, we get:
3/18 + 2/18 = 1/x
5/18 = 1/x
Cross multiplying, we get:
5x = 18
x = 18/5
x = 3.6
Therefore, it will take Irina and Paulo 3.6 hours to paint the room together.