Question

After hitting a plot twist in his new mystery novel, Kendrick can't wait to find out who the villain is. So far, he spent 3 hours reading the first 165 pages. If Kendrick 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. minutes

Answer 1

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.

\[
\boxed{36}
\]