Question

Daniel and Audrey are reading the same book. At the beginning of the month, Daniel was on page 49 and Audrey was on page 22. Daniel will read 17 pages per day and Audrey will read 20 pages per day. Let D represent the page of the book that Daniel is on at the end of t days into the month, and let A represent the page of the book that Audrey is on at the end of t days into the month. Write an equation for each situation, in terms of t, and determine what page Daniel and Audrey will be on on the day they are both on the same page.

Answer 1

Daniel's and Audrey's progress in reading a book can be represented by the equations D = 49 + 17t and A = 22 + 20t, respectively. Solving these equations determines that they will both be on page 202 after 9 days.

Step-by-step explanation:

We need to find the equations that represent the page number that Daniel and Audrey are on after t days, and then determine when they will be on the same page. For Daniel, since he starts on page 49 and reads 17 pages per day, his equation can be represented as D = 49 + 17t. Similarly, for Audrey, who starts on page 22 and reads 20 pages per day, her equation can be represented as A = 22 + 20t.

To find out when they will be on the same page, we set these two equations equal to each other:

49 + 17t = 22 + 20t

By solving for t, we subtract 17t from both sides:

49 = 22 + 3t

Then, subtract 22 from both sides:

27 = 3t

Divide both sides by 3:

t = 9

So, after 9 days, they will be on the same page. To find out which page they will be on, plug t = 9 back into Daniel's equation:

D = 49 + 17(9) = 49 + 153 = 202

Therefore, both Daniel and Audrey will be on page 202 after 9 days.