To solve this problem using a model-drawing or algebraic approach, let's define:

• Let S be the son's current age.
• Let F be the father's current age.

We are given the following relationships:

1. The son's present age is half the difference between the father's and the son's ages:

   $S = \frac{1}{2}(F - S)$

2. Four years ago, the son's age was one-third the difference between the father's and son's ages at that time:

   $S - 4 = \frac{1}{3}(F - S - 4)$

3. In the future, the son's age will be one-quarter the difference between the father's age and the son's age:

   $S = \frac{1}{4}(F - S)$

Let's now break this down and solve it step by step.

Step 1: Equation from the first condition

From the first condition, $S = \frac{1}{2}(F - S)$, multiply both sides by 2 to eliminate the fraction:

$2S = F - S$

Now, rearrange this to express $F$ in terms of $S$:

$F = 3S$

Step 2: Equation from the second condition

From the second condition, $S - 4 = \frac{1}{3}(F - S - 4)$, substitute $F = 3S$ into this equation:

$S - 4 = \frac{1}{3}((3S) - S - 4)$

Simplify the right-hand side:

$S - 4 = \frac{1}{3}(2S - 4)$

Multiply both sides by 3 to eliminate the fraction:

$3(S - 4) = 2S - 4$

Expand both sides:

$3S - 12 = 2S - 4$

Now solve for $S$:

$3S - 2S = -4 + 12$

$S = 8$

Step 3: Find the father's age

Now that we know the son's age $S = 8$, substitute this into $F = 3S$ to find the father's age:

$F = 3(8) = 24$

Conclusion:

The father's current age is 24 years.

Would you like to discuss further details or have any additional questions?

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Here are some related questions you might find useful:

1. How can the relationships between ages be expressed graphically?
2. What if the son's age was expressed as a fraction of the father's age?
3. How do algebraic techniques help in solving real-life word problems?
4. How would the problem change if the age difference was given explicitly?
5. Can this problem be solved using systems of equations involving more variables?

Tip: When solving word problems, identifying the key relationships between variables and expressing them algebraically helps break down the problem into manageable steps.