Joan and Jett are installing new floors in their house. Working alone, Joan can complete the floor in 12 hours. Jett can complete the same floor In 9 hours if working alone. How long will it take them, working together, to finish the floor? Round your answer the the nearest hundredth if necessary.

Answer 1

To find the time it will take Joan and Jett to finish the floor together, we can use the formula:

1 / (time it takes Joan + time it takes Jett) = Combined rate

Let x be the time it takes for Joan and Jett to finish the floor together.

Joan's rate = 1 floor / 12 hours = 1/12
Jett's rate = 1 floor / 9 hours = 1/9
Combined rate = 1/x

1/12 + 1/9 = 1/x
(3/36) + (4/36) = 1/x
7/36 = 1/x

Cross multiply:
7x = 36
x = 36/7
x ≈ 5.14 hours

Therefore, it will take Joan and Jett approximately 5.14 hours to finish the floor together.