# Ratio, Proportion and Percentages Puzzle -Critical Thinking 10

This is another fun critical thinking puzzle to encourage logic and problem-solving. ## Challenge:

Amanda and Dani can paint a room together in 6 hours. If Amanda can paint the room by herself in 8 hours, what percent of the painting does Dani do?

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Amanda can paint the room by herself in 8 hours. Therefore, she can paint $$\frac{1}{8}$$ of the room in an hour. In the same way, Dani can paint $$\frac{1}{x}$$ of the room in an hour. Together, they can paint $$\frac{1}{6}$$ part of the room in an hour. Now, write the equation and solve for x.
$$\frac{1}{8}+\frac{1}{x}=\frac{1}{6}⇒\frac{1}{6}-\frac{1}{8}=\frac{1}{24}⇒x=24$$
Dani can paint the room in 24 hours. Then, in six hours, Dani paints $$\frac{6}{24}$$ or $$\frac{1}{4}$$ part or 25% of the room.

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