Problem:
The students in Mrs. Reed's English class are reading the same -page novel. Three friends, Alice, Bob and Chandra, are in the class. Alice reads a page in seconds, Bob reads a page in seconds and Chandra reads a page in seconds.
Chandra and Bob, who each have a copy of the book, decide that they can save time by "team reading" the novel. In this scheme, Chandra will read from page to a certain page and Bob will read from the next page through page , finishing the book. When they are through they will tell each other about the part they read. What is the last page that Chandra should read so that she and Bob spend the same amount of time reading the novel?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
The ratio of time it takes Bob to read a page to the time it takes Chandra to read a page is or , so Bob should read of the number of pages that Chandra reads. Divide the book into parts, each with pages. Chandra will read the first pages, while Bob reads the last pages.
If Chandra reads pages, she will read for seconds. Bob has to read pages, and this takes him seconds. Because Chandra and Bob read the same amount of time, .
Solving for ,
So Chandra will read the first pages.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions