1. Andrija read a book over three days. While reading, his reading speed was constant. On the first day, he spent $\frac{1}{32}$ of a day reading, and each subsequent day he read for one-third less time than the previous day. What percentage of the book does Andrija still need to read if it takes him 1 hour and 40 minutes to read the entire book?
1. Andrija read a book over three days. While reading, his reading speed was constant. On the first day, he spent $\frac{1}{32}$ of a day reading, and each subsequent day he read for one-third less time than the previous day. What percentage of the book does Andrija still need to read if it takes him 1 hour and 40 minutes to read the entire book?

## Solution.

1 day has 24 hours or $24 \cdot 60=1440$ minutes.

Andrija spent $\frac{1}{32}$ of a day reading on the first day, which is $1440: 32=45$ minutes. $\quad 1$ POINT One-third of 45 is 15, so he spent $45-15=30$ minutes reading on the second day. 2 POINTS One-third of 30 is 10, so he spent $30-10=20$ minutes reading on the third day. $\quad 2$ POINTS Over the three days, Andrija spent a total of $45+30+20=95$ minutes reading. 1 POINT Andrija needs 1 hour and 40 minutes to read the entire book, which is $60+40=100$ minutes.

To finish reading the entire book, he still needs to read for $100-95=5$ minutes. 1 POINT

Expressed as a percentage, this is $\frac{5}{100}=5 \%$.

1 POINT

Andrija still needs to read $5 \%$ of the book.

TOTAL 10 POINTS