Armand is an urban planner, and he has proposed a site for a new town library. The site is between City Hall and the post office on Main Street.

The distance between City Hall and the post office is 6\(\frac{1}{2}\) miles. City Hall is 1\(\frac{1}{4}\) miles closer to the library site than it is to the post office.

a. Write 6\(\frac{1}{2}\) miles and 1\(\frac{1}{4}\) miles as decimals

b. Let d represent the distance from City Hall to the library site. Write an expression for the distance from the library site to the post office.

c. Write an equation that represents the following statement: The distance from City Hall to the library site plus the distance from the library site to the post office is equal to the distance from City Hall to the post office.

d. Solve your equation from part c to determine the distance from City Hall to the library site, and the distance from the post office to the library site.

Sumaya is reading a book with 288 pages. She has already read 90 pages. She plans to read 20 more pages each day until she finishes the book.

a. Sumaya writes the equation 378 = -20d to find the number of days she will need to finish the book. Identify the errors that Sumaya made.

b. Write and solve an equation to determine how many days Sumaya will need to finish the book. In your answer, count part of a day as a full day. Show that your answer is reasonable.

c. Estimate how many days you would need to read a book about the same length as Sumaya’s book. What information did you use to find the estimate?