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Painting in shifts

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Marko alone can paint a fence in $10$ hours, and Dana alone can paint it in $15$ hours, each at a constant rate. Marko paints alone for $4$ hours and then leaves, and Dana finishes the rest alone. How many hours does Dana paint?

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Hint

Find the share of the fence left after Marko leaves.

Solution

Marko paints $\frac{1}{10}$ of the fence per hour, so in $4$ hours he paints $\frac{4}{10} = \frac{2}{5}$ .
That leaves $1 - \frac{2}{5} = \frac{3}{5}$ of the fence.
Dana paints $\frac{1}{15}$ per hour, so she needs $\frac{3}{5} \times 15 = 9$ hours.
So Dana paints for $9$ hours.

Answer: $9$

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