Multiply the amount of pages by the amount of words per page:
[tex] 820 \times 350 = 287000 [/tex]
There are about 287000 words remaining.
Courtney can read at a rate of 110 words per minute. Since we want to find the amount of hours she needs to finish the book, multiply this rate by 60 to convert into an hour:
[tex] 110 \times 60 = 6600 [/tex]
Courtney reads at a rate of 6600 words per hour.
Divide the amount of words in the book by Courtney's reading speed in hours:
[tex] 287000 \div 6600 = \boxed{43.48} [/tex]
Courtney will need to set aside 43.48 hours to complete her assignment.