Let's break down the problem step by step.

Step 1: Time to read one page

Ben reads $\frac{1}{4}$ of a page in $\frac{1}{3}$ of a minute.

To find how long it takes him to read one full page, we can set up a proportion:

$\frac{\text{time to read 1 page}}{\text{time to read } \frac{1}{4} \text{ of a page}} = \frac{\text{1 page}}{\frac{1}{4} \text{ page}}$

This becomes:

$\frac{\text{time to read 1 page}}{\frac{1}{3} \text{ minute}} = \frac{1}{\frac{1}{4}}$

Simplifying the right side:

$\frac{1}{\frac{1}{4}} = 4$

Thus, the time to read one page is:

$\text{Time to read 1 page} = 4 \times \frac{1}{3} = \frac{4}{3} \text{ minutes}.$

So, it will take Ben $\frac{4}{3}$ minutes, or approximately 1 minute and 20 seconds, to read one page.

Step 2: Time to read the entire book

The book has 12 chapters, and each chapter is 20 pages long. Therefore, the total number of pages in the book is:

$\text{Total pages} = 12 \times 20 = 240 \text{ pages}.$

Now, we know Ben takes $\frac{4}{3}$ minutes to read one page, so the total time to read the book is:

$\text{Total time} = 240 \times \frac{4}{3} = 320 \text{ minutes}.$

Thus, it will take Ben 320 minutes to read the entire book.

Conclusion:

• Ben takes $\frac{4}{3}$ minutes to read one page.
• It will take him 320 minutes to read the entire book.

Would you like more details or have any questions?

Here are 5 related questions:

1. How long would it take Ben to read half of a chapter?
2. If Ben increases his reading speed by 20%, how much time will he save for the whole book?
3. How many chapters can Ben read in 2 hours?
4. If each chapter had 25 pages, how much longer would the total reading time be?
5. How many pages can Ben read in 10 minutes?

Tip: To handle rates like this, setting up proportions helps clarify the relationships between time and quantity (pages, in this case).