Ava and Wyatt are reading the same book. At the beginning of the month, Ava was on page 10 and Wyatt was on page 30. Ava will read 20 pages per day and Wyatt will read 15 pages per day. Let AA represent the page of the book that Ava is on at the end of tt days into the month, and let WW represent the page of the book that Wyatt is on at the end of tt days into the month. Graph each function and determine after how many days, t, commat, Ava and Wyatt will be on the same page of the book.

Answer 1

Let's define the functions for Ava's and Wyatt's pages as follows:

1. Ava's Page:

   • Ava starts on page 10 and reads 20 pages per day. Therefore, after \( t \) days, Ava's page can be represented by the function: \[ AA(t) = 10 + 20t \]

2. Wyatt's Page:

   • Wyatt starts on page 30 and reads 15 pages per day. Therefore, after \( t \) days, Wyatt's page can be represented by the function: \[ WW(t) = 30 + 15t \]

Finding the Intersection

To determine when Ava and Wyatt will be on the same page, we need to set the two equations equal to each other and solve for \( t \): \[ 10 + 20t = 30 + 15t \]

Now, isolate the variable \( t \):

1. Subtract \( 15t \) from both sides: \[ 10 + 20t - 15t = 30 \] \[ 10 + 5t = 30 \]

2. Subtract 10 from both sides: \[ 5t = 20 \]

3. Divide both sides by 5: \[ t = 4 \]

Conclusion

Therefore, after \( t = 4 \) days, Ava and Wyatt will be on the same page in the book.

Verifying:

Now let's check the page numbers after 4 days:

• Ava: \[ AA(4) = 10 + 20 \cdot 4 = 10 + 80 = 90 \]

• Wyatt: \[ WW(4) = 30 + 15 \cdot 4 = 30 + 60 = 90 \]

Both are on page 90. Thus, the solution is confirmed: they will be on the same page after \( t = 4 \) days.