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Please explain this. Hello, I'm terrible at word problems, and I was hoping someone could give me the written equation and explain why for this word problem. (NOT FULLY WORKED OUT to answer) Here is the problem "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."

Thanks in advance!

Respuesta :

hallison342

Answer:

Anita cleans 1/8 of the pool each hour and Chao cleans 1/5 of the pool each hour.

[tex]\frac{x}{8}[/tex] + [tex]\frac{x}{6}[/tex] = [tex]\frac{7}{24}[/tex]

then you take [tex]\frac{1}{(7/4}[/tex] = [tex]\frac{27}{7}[/tex]

your answer will be

Step-by-step explanation:

luisejr77

Answer:

[tex]t =\frac{24}{7}\ hours[/tex]

Step-by-step explanation:

For these types of problems use the following formula.

[tex]\frac{t}{x}+\frac{t}{z} =1[/tex]

Where t is the time it takes them both to clean the entire pool if they work together.

x is the time it takes Anita to clean the pool

z is the time it takes Chao to clean the pool

So:

[tex]\frac{t}{8}+\frac{t}{6} =1[/tex]

Now solve the equation for t

[tex]\frac{7}{24}t =1[/tex]

[tex]t =\frac{24}{7}\ hours[/tex]

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