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.
Please and thank you for the help!
add up the fraction of the job done by each in one hour.
If they can do the job together in x hours, then
1/x = 1/6 + 1/8
Now just find x.
To find the time it would take Anita and Chao to clean the pool together, we need to calculate their combined work rate.
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, we add their individual work rates:
1/8 + 1/6 = (3/24) + (4/24) = 7/24.
Their combined work rate is 7/24 of a pool per hour.
To find the time it takes for Anita and Chao to clean the pool together, we divide the total work (1 pool) by their combined work rate (7/24 pool per hour):
1 / (7/24) = 24/7.
Therefore, it would take Anita and Chao approximately 24/7 hours to clean the pool together.
To solve this problem, we can use the concept of rates and the formula:
Rate x Time = Work
Let's assume that the work is cleaning a typical pool. We know that Anita can clean a typical pool in 8 hours, which means her rate of work is 1/8 of a pool per hour. Similarly, Chao can clean a typical pool in 6 hours, so his rate of work is 1/6 of a pool per hour.
Let's determine the combined rate of Anita and Chao when they work together. Since they are working on the same pool, their rates of work are additive. So the combined rate is:
(1/8) + (1/6)
To add these fractions, we need to find a common denominator. Multiplying the denominators, 8 and 6, gives us 48. Now we can rewrite the fractions with the common denominator:
(3/24) + (4/24)
Combining the fractions, we have:
7/24
Therefore, when Anita and Chao work together, their combined rate is 7/24 of a pool per hour.
Now, let's use this combined rate to determine how long it would take Anita and Chao to clean a typical pool together. We can rearrange the formula Rate x Time = Work to solve for Time:
Time = Work / Rate
In this case, the work is 1 pool and the rate is 7/24 of a pool per hour. Substituting these values, we have:
Time = 1 / (7/24)
To divide by a fraction, we can multiply by its reciprocal. The reciprocal of 7/24 is 24/7. So:
Time = 1 x (24/7)
Multiplying the numerators and denominators, we get:
Time = 24/7
Therefore, it should take Anita and Chao working together approximately 24/7 hours to clean a typical pool.