First, we need to determine Kendrick's reading rate based on the information provided. He has read 165 pages in 3 hours.
First, convert 3 hours into minutes:
\[ 3 \text{ hours} = 3 \times 60 = 180 \text{ minutes} \]
Now, calculate his reading rate in pages per minute:
\[ \text{Reading rate} = \frac{165 \text{ pages}}{180 \text{ minutes}} = \frac{165}{180} \text{ pages per minute} \]
Next, simplify \(\frac{165}{180}\):
To simplify it, find the greatest common divisor (GCD) of 165 and 180. The prime factorization of 165 is \(3 \times 5 \times 11\) and for 180 it is \(2^2 \times 3^2 \times 5\). The common factors are \(3\) and \(5\), so the GCD is \(15\).
Now divide both the numerator and the denominator by their GCD:
\[ \frac{165 \div 15}{180 \div 15} = \frac{11}{12} \]
Thus, Kendrick reads at a rate of \(\frac{11}{12}\) pages per minute.
Now, we need to find out how many pages Kendrick has left to read in the 198-page book:
\[ \text{Pages left to read} = 198 \text{ pages} - 165 \text{ pages} = 33 \text{ pages} \]
To find out how long it will take him to read these remaining 33 pages, use his reading rate:
\[ \text{Time required} = \text{Pages left} \div \text{Reading rate} = \frac{33 \text{ pages}}{\frac{11}{12} \text{ pages per minute}} = 33 \times \frac{12}{11} \]
Perform the multiplication:
\[ = \frac{33 \times 12}{11} = \frac{396}{11} = 36 \text{ minutes} \]
Therefore, Kendrick will need 36 minutes more to finish the book.
\[ \boxed{36} \]
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