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 work rate: 1 pool per 8 hours = 1/8 pool per hour
Chao's work rate: 1 pool per 6 hours = 1/6 pool per hour
Working together: (1/8 + 1/6) pools per hour = (3/24 + 4/24) pools per hour = 7/24 pools per hour
To clean 1 pool, the time it takes working together is: 1 / (7/24) hours = 24/7 hours = 3 3/7 hours, or approximately 3 hours and 26 minutes.
Therefore, it would take Anita and Chao working together approximately 3 hours and 26 minutes to clean a typical pool.
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To solve this problem, we can use the concept of work rate. The work rate is determined by the inverse of the time it takes to complete a task.
First, let's find the work rates for Anita and Chao individually. Anita can clean a pool in 8 hours, so her work rate is 1/8 of a pool per hour. Chao can clean a pool in 6 hours, so his work rate is 1/6 of a pool per hour.
To find their combined work rate when working together, we need to add up their individual work rates. So, the combined work rate is:
1/8 + 1/6 = 3/24 + 4/24 = 7/24 of a pool per hour.
To find out how long it would take Anita and Chao to clean a pool together, we divide the total work (1 pool) by their combined work rate (7/24 pool per hour). This can be calculated as:
1 รท (7/24) = 24/7.
Therefore, it would take Anita and Chao working together approximately 24/7 hours to clean a typical pool. This can be reduced to a mixed number as 3 3/7 hours.