Valeria and Autumn are reading the same book. At the beginning of the month, Valeria was on page 20 and Autumn was on page 40. Valeria will read 20 pages per day and Autumn will read 15 pages per day. Let VV represent the page of the book that Valeria is on at the end of tt days into the month, and let AA represent the page of the book that Autumn is on at the end of tt days into the month. Graph each function and determine after how many days, t, commat, Valeria and Autumn will be on the same page of the book.    Put it on a graph


The graph above shows the reading progress of Valeria and Autumn over time, based on their reading rates. From the plot, we can observe that their progress lines intersect at a point.

To determine the exact day when they will be on the same page, I solved the equation for \( t \), where the pages they are on are equal:

\[
20 + 20t = 40 + 15t
\]

Solving for \( t \), we find:

\[
t = 4
\]

So, after 4 days, Valeria and Autumn will be on the same page of the book.

Would you like more details or have any other questions?

Here are 5 related questions for further practice:
1. What page will Valeria and Autumn be on after 4 days?
2. How many days will it take for Valeria to finish reading 100 pages?
3. What is the difference in pages between Valeria and Autumn after 2 days?
4. If Autumn starts reading 5 pages faster per day, after how many days will they meet?
5. How many pages will Valeria have read after 6 days?

**Tip**: When solving for the intersection of two linear equations, equate them and solve for the variable representing the independent term (in this case, time \( t \)).

Valeria and Autumn are reading the same book. At the beginning of the month, Valeria was on page 20 and Autumn was on page 40. Valeria will read 20 pages per day and Autumn will read 15 pages per day. Let VV represent the page of the book that Valeria is on at the end of tt days into the month, and let AA represent the page of the book that Autumn is on at the end of tt days into the month. Graph each function and determine after how many days, t, Valeria and Autumn will be on the same page of the book.

Graph the reading progress of Valeria and Autumn as they read a book at different rates. Valeria reads 20 pages per day, while Autumn reads 15 pages per day. Learn how to solve a system of linear equations to find when they'll be on the same page. Suitable for Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation