Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. Anita can clean a typical pool in 8 hours. Chao can clean a typical pool in 6 hours. How long should it take Anita and Chao working together to clean a typical pool? Show all your work. Leave your final answer as an integer or reduced fraction.
To find how long it will take Anita and Chao to clean a pool together, we can use the formula:
\(\frac{1}{t} = \frac{1}{a} + \frac{1}{c}\)
where:
t = time it takes for Anita and Chao to clean the pool together
a = time Anita takes to clean the pool alone
c = time Chao takes to clean the pool alone
Plugging in the values:
\(\frac{1}{t} = \frac{1}{8} + \frac{1}{6}\)
\(\frac{1}{t} = \frac{3}{24} + \frac{4}{24}\)
\(\frac{1}{t} = \frac{7}{24}\)
Now, solving for t:
t = \(\frac{24}{7}\)
Therefore, it will take Anita and Chao approximately 3 \(\frac{3}{7}\) hours to clean a pool together.