Question

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.?

Answer 1

if he started reading from where he left off, and it's 5:30 and he is at page 160, and then he got to page 280 by 8:00, that is 2 hours and 30 minutes. so bring the reading time down into easier numbers so that 5-> 30 minute terms, then find out how many pages he read in 30 minutes. The difference between 160 pages and 280 pages is 120 pages. 120 divided by 30 equals 4. the amount of time between 3:30 and 5:30 is 2 hours which is 4-> 30 minute terms. So if it takes 30 minutes to read 4 pages then multiply 4 with 4 which equals 16, and finally subtract 16 from 160 and that's going to equal 144 pages.

(Sorry about the paragraph but i figured ide give you my reasoning and work just in case if i was wrong, ide like to know what i did if i am wrong. And if I'm right then that's how you show your work!)

Answer 2

To find the time Casey read today, 5:30 from 8:00.
8:00 - 5:30 = 2:30
Casey

To find the number of pages Casey read today subtract the page number he started reading on to the page he stopped on.
280 - 160 = 120
Casey read 120 pages today.

Now you need to find how many pages Casey read in one hour.

If Casey read 120 pages in 2.5 hours, you can find how many pages he read in one hour by dividing 120 by 2.5.
120 ÷ 2.5 = 48.
Casey read 48 pages in one hour.

Casey was on page 160 at 5:30, and you need to find what page he was on at 3:30. Since Casey read for 2 hours before he reached page 160, you need to subtract 2 hours worth of reading from that number.

160 - (2×48)
160 - 96
64


Casey was on page 64 at 3:30 pm today.