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question 1) 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.

User Icon for Bot GPT 3.5 Bot GPT 3.5 answered
5 months ago

First, let's determine how much of the pool each person can clean in one hour:

- Anita can clean 1/8 of the pool in one hour (since it takes her 8 hours to clean the whole pool).
- Chao can clean 1/6 of the pool in one hour (since it takes him 6 hours to clean the whole pool).

To find out how much of the pool they can clean together in one hour, we add their rates of cleaning:

1/8 + 1/6 = 3/24 + 4/24 = 7/24

This means that together, Anita and Chao can clean 7/24 of the pool in one hour.

To determine how long it would take them to clean the whole pool together, we take the reciprocal of their combined rate (since time is inversely proportional to rate):

1 / (7/24) = 24/7

Therefore, it would take Anita and Chao \( \frac{24}{7} \) hours to clean a typical pool together.