Question

Sophie and Jackson are reading the same book. At the beginning of the month, Sophie was on page 20 and Jackson was on page 50. Sophie will read 10 pages per day and Jackson will read 5 pages per day. Let S represent the page of the book that Sophie is on at the end of t days into the month, and let J represent the page of the book that Jackson is on at the end of t days into the month. Graph each function and determine after how many days t Sophie and Jackson will be on the same page of the book.

Answer 1

t = 6 days

Explanation:

We can model both cases with linear equations in the form:

y = ax + b

Sophie was on page 20 and she reads 10 pages per day, so her equation is:

S = 20 + 10t

Jackson was on page 50 and he reads 5 pages per day, so his equation is:

J = 50 + 5*t

The graph of those equations are in the image attached (The blue line is for Sophie and the orange line is for Jackson)

To find after how many days they will be on the same page, we can make S = J and then find the value of t:

20 + 10t = 50 + 5t

5t = 30

t = 6 days