Kane 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 1/4 mile.

Question

Let w be the number of weeks. Write an expression to show the distance Kane runs in a training session after w weeks.

Answer 1

Kane starts by running 3 miles in his first training session. Each week, he increases his distance by 1/4 mile. We can represent the distance he runs after \( w \) weeks with the following expression:

\[ \text{Distance after } w \text{ weeks} = 3 + \left( \frac{1}{4} \times w \right) \]

So the expression for the distance Kane runs in a training session after \( w \) weeks is:

\[ 3 + \frac{1}{4}w \]