Final answer:
The distance Kane runs in a training session after w weeks can be represented by the equation D = 3 + (1/4)w, where D is the total distance run in miles, and w represents the number of weeks.
Step-by-step explanation:
Kane's training sessions begin with a distance of 3 miles. As he increases his running distance by adding 1/4 mile each week, we can build an equation to represent this situation by combining the initial distance with the additional distance he runs each week. This equation is represented as D = 3 + (1/4)w.
In this equation, D represents the total distance run in miles, 3 is the initial distance run, 1/4 represents the increase in distance each week, and w represents the number of weeks.
For example, if Kane has been training for 2 weeks, we would substitute 2 for w, to get D = 3 + (1/4)(2), which simplifies to D = 3.5 miles. This means after 2 weeks, Kane would run 3.5 miles in a training session. Similarly, if Kane has been training for 4 weeks, we substitute 4 for w, to get D = 3 + (1/4)(4), and this simplifies to D = 4 miles. Therefore, the expression 3 + (1/4)w can be used to determine the distance Kane will run in a training session after w weeks.