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Kalon and his friend Marna own a chimney sweep service company. Working together, they can clean a chimney in 1 5/7 hours. If it takes Kalon 4 hours to clean a 20-foot chimney by himself, how long does it take Marna to clean the same size chimney by herself?

Verified Answer :

meerkat18

The amount of work done by Kalon in an hour is equal to 1/4. This is based on his time to finish the job. Letting x be the number of hours Marna can finish the job alone will let her finish 1/x of the job in an hour. If their rates are added together and multiplied by the number of hours they worked together, the product should be one whole job.
                          (1/4 + 1/x)(1 5/7) = 1
The value of x is 3. Therefore, it will take 3 hours for Marna to clean the chimney alone.

Answer:

It takes 3 hours for Marna to clean the same size chimney by herself.

Step-by-step explanation:

Kalon and his friend Marna can clean a chimney in \(1 \frac{5}{7}= \frac{12}{7}\)hours

They can do a part of work in 1 hour = \(\frac{1}{\frac{12}{7}} = \frac{7}{12}\)

Kalon can complete work in 4 hours

He can do a part of work in 1 hour = \(\frac{1}{4}\)

So,  Marna  can do a part of work in 1 hour =  \(\frac{7}{12}-\frac{1}{4}\)

                                                                       =  \(\frac{1}{3}\)

So, Marna can \(\frac{1}{3}\) part of work in hour = 1

Marna can complete work in hour = 3

Hence it takes 3 hours for Marna to clean the same size chimney by herself.

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