Let's denote the age of Sara as \( S \) and the age of her youngest brother as \( B \).
According to the information given:
-
Sara is twice as old as her youngest brother: \[ S = 2B \]
-
The difference between their ages is 15 years: \[ S - B = 15 \]
Now we can use these two equations to solve for \( B \).
Substituting the first equation into the second equation:
\[ 2B - B = 15 \]
This simplifies to:
\[ B = 15 \]
Now that we have the age of the youngest brother, we can find Sara's age:
\[ S = 2B = 2 \times 15 = 30 \]
So, Sara is 30 years old, and her youngest brother is \( \textbf{15 years old} \).