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
Anita's rate: 1 pool / 8 hours = 1/8 pool per hour
Chao's rate: 1 pool / 6 hours = 1/6 pool per hour
Combined rate: (1/8 + 1/6) pool per hour = 7/24 pool per hour
To clean one pool together, they need (1 pool) / (7/24 pool per hour) = 24/7 hours
Reducing this fraction: 24/7 = 3 and 3/7 hours
Therefore, it should take Anita and Chao working together 3 and 3/7 hours (or 3.43 hours rounded to two decimal places) to clean a typical pool.
To find out how long it would take Anita and Chao to clean a typical pool together, we can use the formula:
1/Time taken by Anita + 1/Time taken by Chao = 1/Time taken together.
Let's substitute the given values into the formula:
1/8 + 1/6 = 1/x
Now, we can find a common denominator and simplify the equation:
(6/48) + (8/48) = 1/x
14/48 = 1/x
To eliminate the fraction, we can cross-multiply:
14x = 48
Now, solve for x:
x = 48/14
Simplifying the fraction:
x = 24/7
Therefore, it would take Anita and Chao, working together, approximately 24/7 hours to clean a typical pool.