Question

18pts please help 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.

Answer 1

Answer:

3 3/7 hours.

Step-by-step explanation:

We work in  rates / hour:

Anita  does 1/8 of the pool in 1 hour and Chao does 1/6 in an hour.

Let x be the time they would clean the pool working together,  then we have:

1/8 + 1/6 = 1/x

3/24 + 4/24 = 1/x

7/24 = 1/x

7x= 24

x = 24/7 hours.

Answer 2

It will take 24/7 ≈ 3.43     (3 hours,  25 minutes, 43 seconds) hours to clean a typical pool Anita and Chao working together.

The typical setup for these work problems is

                         $\frac{t}{a}+\frac{t}{b} =1$

Here, a and b are how long they can do it by themselves, and t is how long they work together.

                      ⇒$\frac{t}{8}+\frac{t}{6} =1$

Now, we will do LCM of 8 and 6 and we get 24;

                     ⇒$\frac{3t+4t}{24} =1$

                     ⇒$\frac{7t}{24}=1$

Now, we will multiply 24 on both sides, and we get;

                    ⇒$7t=24$

Now, we will divide by 7 on both sides, we get:

                   ⇒$t=\frac{24}7}$

Hence, the answer is $\frac{24}7}$ hours.

x=24/7 ≈ 3.43     (3 hours,  25 minutes, 43 seconds)

What is least common multiple?

In arithmetic and number theory, the least common multiple, lowest common multiple, or smallest common multiple of two integers a and b, usually denoted by lcm(a, b), is the smallest positive integer that is divisible by both a and b.

What is the LCM of 3 and 8?

The lowest common multiple of 3 and 8? Multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24... Multiples of 8 are 8, 16, 24, 32, 40... So the lowest common multiple of 3 and 8 is 24.

Learn more about  the least common multiple, refer to:

https://brainly.com/question/20521181

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