Casey is reading a book for a book report. at 3: 30 p. m., he started reading where he had left off the day before. at 5: 30 p. m. he was on page 160. at 8: 00 p. m. he was on page 280. if reading the book is modeled by a linear function, what page did casey start on at 3: 30 p. m.?

At 3.30 pm he started reading where he left off.

At 5.30 pm he is at page 160

At 8.00 pm he is at page 280

Between 5.30 pm and 8.00 pm he has covered  = 280 - 160 = 120 pages

That is in between (8.00 - 5.30) = 2 hours 30 minutes = 2 and 1/2 hours

= 2.5 hours

Therefore he covered 120 pages in 2.5 hours, this would be used to set up the linear function.

Between 3.30 pm and 5.30 pm is (5.30 - 3.30) = 2 hours

We need to find how many pages can be covered in 2 hours.

In 2.5 hours      120 pages were covered.

In 1 hour      =    120 / 2.5 =  48 pages.

In 2 hours    =    48 * 2 = 96 pages.

If he went at the same rate, that means at 2 hours before 5.30 which is the 3.30, he would have covered 96 pages

Page number =  160 - 96 = 64,  Since he was at 160 at 5.30

So he started at page 64 at 3:30 pm

Whose mistake? can you give more details to what the question is asking?