Question

Kane is training for a marathon. He starts by running 3 miles during every training session each week plans to increase the distance of his runs by 1/4 mile. Let w be the number of weeks. Write and expression to show the diatance kane runs in a training session after w weeks

Answer 1

Answer:

$T_w = \frac{11 + w}{4}$

Step-by-step explanation:

Given

$Starts = 3 miles$

$Difference = \frac{1}{4}\ mile$

Required

Determine the distance for w weeks

This will be calculated using the following Arithmetic progression formula

$T_n = a +(n -1) d$

Where

$a =3$

$n = w$

$d = \frac{1}{4}$

Substitute these values

$T_w = 3 + (w - 1)* \frac{1}{4}$

Open Bracket

$T_w = 3 + \frac{1}{4}w - \frac{1}{4}$

Collect Like Terms

$T_w = 3 - \frac{1}{4} + \frac{1}{4}w$

$T_w = \frac{11}{4} + \frac{1}{4}w$

Take LCM

$T_w = \frac{11 + w}{4}$