Question

morgan and easton are reading the same book. at the beginning of the month, morgan was on page 5 and easton was on page 50. morgan will read 20 pages per day and easton will read 5 pages per day. let m represent the page of the book that morgan is on at the end of t days into the month, and let e represent the page of the book that easton is on at the end of t days into the month. graph each function and determine what page morgan and easton will be on at the time they are both on the same page.

click twice to plot each line. click a line to delete it.

(graph with y-axis labeled page of book from 5 to 100 and x-axis labeled number of days from 0 to 20)

Explanation:

Step1: Define the functions for M and E

Morgan starts at page 5 and reads 20 pages per day, so \( M = 5 + 20t \). Easton starts at page 50 and reads 5 pages per day, so \( E = 50 + 5t \).

Step2: Set M equal to E to find t

To find when they are on the same page, set \( 5 + 20t = 50 + 5t \). Subtract \( 5t \) from both sides: \( 5 + 15t = 50 \). Then subtract 5: \( 15t = 45 \). Divide by 15: \( t = 3 \) days.

Step3: Find the page number

Substitute \( t = 3 \) into either M or E. Using M: \( M = 5 + 20(3) = 5 + 60 = 65 \). Or using E: \( E = 50 + 5(3) = 50 + 15 = 65 \).

Answer:

They will both be on page 65.