Question

Matthew is training to participate in a half marathon. The table below shows the number of miles he runs in weeks 1 and 2. Week Number of Miles Run 1 12.5 2 13.5 Each week, Matthew increases the number of miles he runs in the previous week by the same percent. How many miles does Matthew run in week 3? Do not round your answer. a0 miles

Answer 1

Answer: There is 14.5 miles run by Matthew in week 3.

Explanation:

Since we have given that

Week Number of miles

1 12.5

2 13.5

First we will find the slope :

(1,12.5) and (2,13.5)

So, Slope would be

`(y_2-y_1)/(x_2-x_1)\\\\=(13.5-12.5)/(2-1)\\\\=1`

So, equation of line would be

`y-y_1=m(x-x_1)\\\\y-12.5=1(x-1)\\\\y-12.5=x-1\\\\y-x=12.5-1\\\\y-x=11.5`

We need to find the number of miles in week 3.

So, we put x = 3,

`y-3=11.5\\\\y=11.5+3\\\\y=14.5`

Hence, there is 14.5 miles run by Matthew in week 3.