2006 AMC 8 Problem 14

Below is the professionally curated solution for Problem 14 of the 2006 AMC 8, 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.

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Concepts:ratedistributive property

Difficulty rating: 980

14.

Problems 14,15,14, 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

Solution:

Bob will take 76045760 \cdot 45 seconds to read the book, and Chandra will take 76030760 \cdot 30 seconds.

The difference between the time they spent reading is 7604576030 760 \cdot 45 - 760 \cdot 30 =760(4530)= 760(45 - 30) =76015= 760 \cdot 15 =11,400= 11,400 seconds.

Thus, B is the correct answer.

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