Question

Jeanette and Carlos are participating in a novel-writing challenge. Jeanette has already started her novel and has written 48 pages so far. She will write an additional 4 pages each week. Carlos is just getting started, and he will write 10 pages each week.
Which equation can you use to find w, the number of weeks it will take for Carlos to write as many pages as Jeanette?
How long will it take for Carlos to have written as many pages as Jeanette?
weeks

Answer 1

To find the number of weeks \( w \) it will take for Carlos to write as many pages as Jeanette, we need to set up an equation based on their writing rates.

Jeanette has already written 48 pages and writes 4 additional pages each week. Therefore, the total number of pages Jeanette will have after \( w \) weeks can be expressed as:
\[
J(w) = 48 + 4w
\]

Carlos, who just started, writes 10 pages each week. Thus, the total number of pages Carlos will have after \( w \) weeks is:
\[
C(w) = 10w
\]

To find out when Carlos will have written as many pages as Jeanette, we set these two expressions equal to each other:

\[
48 + 4w = 10w
\]

Now, we can solve for \( w \):

1. Rearranging the equation:
\[
48 = 10w - 4w
\]
\[
48 = 6w
\]

2. Dividing both sides by 6:
\[
w = \frac{48}{6} = 8
\]

Therefore, it will take Carlos **8 weeks** to write as many pages as Jeanette.