Jose and Aubree are reading the same book. At the beginning of the month, Jose was on page 5 and Aubree was on page 25. Jose will read 14 pages per day and Aubree will read 10 pages per day. Let
J
J represent the page of the book that Jose is on at the end of
t
t days into the month, and let
A
A represent the page of the book that Aubree is on at the end of
t
t days into the month. Write an equation for each situation, in terms of
t
,
t, and determine what page Jose and Aubree will be on on the day they are both on the same page.

Let J(t) represent Juan's equation and A(t) represent Aubree's equation. If Juan starts this venture on page 5, even if he didn't read any more days at all, when t = 0, he would still have read those 5 pages. Because he reads 14 pages per day, then he reads 14t and t represents the number of days gone by. His equation then is

J(t) = 14t + 5

Likewise, for Aubree, even if she decides not to read any more past the original 25 pages she started with, she would still have read those 25 pages. Her equation then would be

A(t) = 10t + 25

We need to know how many days will go by before they are both on the same page, so set the equations equal to each other and solve for t:

14t + 5 = 10t + 25 and

4t = 20 so

t = 5

After 5 days they will have both read the same number of pages.