A $420$-page book contains an average of $600$ words per page, and Roslyn reads the book at the rate of $360$ words per minute. How many hours did it take her to read the book? Express your answer as a mixed number.

To determine how many hours it took Roslyn to read the book, we need to follow these steps:

1. **Calculate the total number of words in the book.**
2. **Determine the total time taken to read the book in minutes.**
3. **Convert the total reading time from minutes to hours and express it as a mixed number.**

First, we calculate the total number of words in the book:

\[
\text{Total words} = \text{Number of pages} \times \text{Words per page}
\]

Given:
\[
\text{Number of pages} = 420, \quad \text{Words per page} = 600
\]

\[
\text{Total words} = 420 \times 600 = 252,000 \text{ words}
\]

Next, we calculate the total time taken to read the book in minutes. Roslyn reads at a rate of 360 words per minute. So, we use the following formula:

\[
\text{Total time (minutes)} = \frac{\text{Total words}}{\text{Words per minute}}
\]

\[
\text{Total time (minutes)} = \frac{252,000 \text{ words}}{360 \text{ words per minute}} = 700 \text{ minutes}
\]

Finally, we convert the total reading time from minutes to hours. We know that there are 60 minutes in an hour, so:

\[
\text{Total time (hours)} = \frac{700 \text{ minutes}}{60 \text{ minutes per hour}}
\]

Dividing, we get:

\[
\text{Total time (hours)} = \frac{700}{60} = \frac{35}{3} \text{ hours}
\]

To express $\frac{35}{3}$ as a mixed number, we perform the division:

\[
35 \div 3 = 11 \text{ remainder } 2
\]

Thus,

\[
\frac{35}{3} = 11 \frac{2}{3}
\]

So, it took Roslyn $11 \frac{2}{3}$ hours to read the book.

Do you want details or have any questions?

Here are 5 more questions you might find interesting:
1. If a car travels at an average speed of 50 mph, how long will it take to travel 300 miles?
2. How many days will it take to read a 600-page book if you read 20 pages per day?
3. If a train travels 400 miles in 5 hours, what is its average speed in miles per hour?
4. How long will it take to fill a 1500-gallon pool with a hose that flows at 10 gallons per minute?
5. What is the distance covered by a person walking at 4 mph for 2 hours and 15 minutes?

Tip: When dealing with large numbers or units, break down the problem into smaller, manageable steps to ensure accuracy.

Learn how to calculate the time taken to read a 420-page book with an average of 600 words per page at a reading rate of 360 words per minute. Includes step-by-step calculations and conversion from minutes to hours.

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