Let \(t\) be the time in hours it took Linda to read the same book. Since Marie can read 200 words in a minute and she took 14 hours to read the book, she read a total of \(200 \times 14 \times 60 = 168000 \) words. Since Linda reads 160 words per minute, she will need to read for
$$t = \frac{168000}{160} = \frac{21000}{20}=1050\ minutes=17.5 \ hours.$$
Therefore, Linda will need 17.5 hours to read the same book.