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

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

1 answer

Tim has read 165 pages in 3 hours. To find out how much time he takes to read one page, we first convert 3 hours into minutes:

\[ 3 \text{ hours} = 3 \times 60 = 180 \text{ minutes} \]

Next, we calculate the rate at which Tim reads:

\[ \text{Reading rate} = \frac{180 \text{ minutes}}{165 \text{ pages}} = \frac{180}{165} = \frac{12}{11} \text{ minutes per page} \]

Now, we need to determine how many pages are left for Tim to read in order to finish the book. The book has a total of 198 pages, and he has already read 165 pages, so:

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

Next, we calculate the time it will take to read these remaining 33 pages:

\[ \text{Time for 33 pages} = 33 \text{ pages} \times \frac{12}{11} \text{ minutes per page} = \frac{33 \times 12}{11} \text{ minutes} \]

Now we perform the multiplication:

\[ 33 \times 12 = 396 \]

Now, divide by 11:

\[ \frac{396}{11} = 36 \text{ minutes} \]

Thus, the number of minutes Tim will need to finish reading the book is:

\[ \boxed{36} \]