Wane is training for a marathon. He starts by running 3 miles during every training session. Each week he plans to increase the distance of his run by $$ \frac{1}{4} $$ mile. Let $$ w $$ be the number of weeks. Write an expression to show the distance Kane runs in a training session after $$ w $$ weeks.

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To find the distance Wane runs in a training session after $$ w $$ weeks, we can start with the initial distance he runs and then add the increase in distance for each week.

1. **Initial Distance**: Wane starts by running 3 miles.
2. **Weekly Increase**: Each week, he increases his distance by $$ \frac{1}{4} $$ mile.

After $$ w $$ weeks, the total increase in distance will be $$ w \times \frac{1}{4} $$ miles.

Now, we can write the expression for the distance $$ D $$ that Wane runs after $$ w $$ weeks:

$$
D = 3 + w \times \frac{1}{4}
$$

This expression shows the distance Wane runs in a training session after $$ w $$ weeks.
The distance Wane runs after $$ w $$ weeks is $$ 3 + \frac{w}{4} $$ miles.

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