After hitting a plot twist in his new mystery novel, David can't wait to find out who the villain is. So far, he spent 3 hours reading the first 165 pages. If David continues to read at the same rate, how many more minutes will he need to finish the 198-page book?

Question

Write your answer as a whole number, decimal, or simplified fraction. Do not round.

Answer 1

David has read 165 pages in 3 hours. To find his reading rate in pages per hour, we calculate:

\[ \text{Reading rate} = \frac{165 \text{ pages}}{3 \text{ hours}} = 55 \text{ pages per hour} \]

Now, the total number of pages in the book is 198. To find out how many more pages David has left to read, we subtract the pages he has already read from the total pages:

\[ \text{Pages left} = 198 \text{ pages} - 165 \text{ pages} = 33 \text{ pages} \]

Next, we need to determine how long it will take him to read the remaining 33 pages at his current reading rate of 55 pages per hour. We can use the formula:

\[ \text{Time} = \frac{\text{Pages}}{\text{Rate}} = \frac{33 \text{ pages}}{55 \text{ pages per hour}} = \frac{33}{55} \text{ hours} \]

To simplify \(\frac{33}{55}\):

\[ \frac{33}{55} = \frac{3}{5} \text{ hours} \]

Now we convert hours into minutes. Since 1 hour equals 60 minutes:

\[ \frac{3}{5} \text{ hours} \times 60 \text{ minutes/hour} = \frac{3 \times 60}{5} = \frac{180}{5} = 36 \text{ minutes} \]

Therefore, David will need 36 more minutes to finish the book.

The final answer is:

\[ \boxed{36} \]