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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After \( w \) weeks, Wane's running distance can be expressed as \( 3 + \frac{1}{4}w \) miles. He starts with 3 miles, and for each week, he's adding \( \frac{1}{4} \) mile to his training session. So, after 1 week, he runs 3.25 miles, after 2 weeks, he runs 3.5 miles, and so on! Getting into a regular running routine can be a blast! Wane might want to set mini-goals along the way to keep himself motivated—like running a local 5K before the marathon. That way, he can celebrate each milestone and gauge his progress on the journey to 26.2 miles!