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The problem states that Robert is half as old as his father. Twelve years ago, Robert was one-third as old as his father was at that time. We are to find their present ages.

Let's denote Robert's current age as \( R \) and his father's current age as \( F \).

From the problem, we have two equations:
1. \( R = \frac{1}{2}F \) (Robert is half as old as his father now)
2. \( R - 12 = \frac{1}{3}(F - 12) \) (Twelve years ago, Robert was one-third as old as his father)

We can solve these equations as follows:
From the first equation, we have \( R = \frac{1}{2}F \). Substituting \( R \) in the second equation, we get:
\[ \frac{1}{2}F - 12 = \frac{1}{3}(F - 12) \]

Let's solve this equation to find \( F \) and \( R \).Robert's current age is 24 years, and his father's current age is 48 years.

Would you like to understand more about how these values were calculated, or do you have any other questions? Here are some related topics you might find interesting:

1. How would the ages change if the ratio of their ages was different?
2. What happens to the age difference as time progresses?
3. How does the solution change if the time frame in the past is altered (e.g., 10 years ago, 15 years ago)?
4. How can this type of problem be represented graphically?
5. What are some real-life applications of solving age-related problems?

**Tip:** When solving age-related algebra problems, defining variables clearly and setting up equations based on relationships and time differences are key steps for successful resolution.

Robert is half as old as his father. Twelve years ago, Robert was one-third as old as his father was. Find their present ages.

Learn how to solve the age problem where Robert is half as old as his father, and twelve years ago, he was one-third his father's age. Detailed algebraic solution suitable for students in Grades 7-9.

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