2006 AMC 8 Problem 14

Attempt Problem 14 of the 2006 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2006 AMC 8 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

14.

Problems 14,14, 15,15, and 1616 involve Mrs. Reed’s English assignment.
A Novel Assignment
The students in Mrs. Reed’s English class are reading the same 760760-page novel. Three friends, Alice, Bob and Chandra, are in the class. Alice reads a page in 2020 seconds, Bob reads a page in 4545 seconds and Chandra reads a page in 3030 seconds.
If Bob and Chandra both read the whole book, Bob will spend how many more seconds reading than Chandra?
7,6007{,}600
11,40011{,}400
12,50012{,}500
15,20015{,}200
22,80022{,}800
Answer: B
Concepts:ratedistributive property
Small hint:
Compare Bob and Chandra by seconds per page.
Big hint:
Bob takes the same extra number of seconds on each of the 760760 pages.
Solution:
Bob will take 760⋅45760 \cdot 45 seconds to read the book, and Chandra will take 760⋅30760 \cdot 30 seconds.
The difference between the time they spent reading is 760⋅45−760⋅30 760 \cdot 45 - 760 \cdot 30 =760(45−30)= 760(45 - 30) =760⋅15= 760 \cdot 15 =11,400= 11,400 seconds.
Thus, B is the correct answer.
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