To determine how long it takes to read a book that has 424 pages, we start with the given equation that relates the total reading time [tex]\( y \)[/tex] in minutes to the number of pages [tex]\( x \)[/tex] read:
[tex]\[ y = \frac{12.4}{20} x \][/tex]
Here, it is given that the time it takes to read 20 pages is 12.4 minutes. This equation can be simplified to:
[tex]\[ y = \frac{12.4}{20} \cdot x \][/tex]
Now, let's find the constant rate of time per page:
[tex]\[ \frac{12.4}{20} = 0.62 \][/tex]
Thus, the simplified equation becomes:
[tex]\[ y = 0.62x \][/tex]
We need to determine the total time [tex]\( y \)[/tex] to read a book with 424 pages ([tex]\( x = 424 \)[/tex]):
[tex]\[ y = 0.62 \cdot 424 \][/tex]
By multiplying the rate of time per page by the number of pages, we get:
[tex]\[ y = 262.88 \][/tex]
Therefore, it will take approximately 262.88 minutes to read a book that has 424 pages.
