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Kalyn and his friend Maria can clean a 20 foot chimney in 1 5/7 hours together. It takes Kalyn 4 hours by himself. How long would it take Maria to clean the chimney by herself?

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Final answer:

It would take Maria approximately 28/41 hours to clean the chimney by herself.

Step-by-step explanation:

To answer this question, we can use the concept of work rates. Let's assume that Maria takes x hours to clean the chimney by herself. In 1 hour, Kalyn can clean 1/4 of the chimney, since it takes him 4 hours to clean the whole chimney. Similarly, in 1 hour, Maria can clean 1/x of the chimney. Working together, in 1 hour, they can clean 1/4 + 1/x of the chimney. We know that together, they can clean the chimney in 1 5/7 hours, or 12/7 hours. Setting up an equation:

1/4 + 1/x = 12/7

We can solve for x by multiplying through by 28x to eliminate the fractions:

7x + 28 = 48x

41x = 28

x = 28/41

Therefore, it would take Maria approximately 28/41 hours to clean the chimney by herself.

User Sindri Traustason
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