Difference between revisions of "2006 AMC 8 Problems/Problem 16"

(Solution)
(Solution)
Line 13: Line 13:
 
==Solution==
 
==Solution==
  
('''C''')
+
'''(e)''' The amount of pages Bob, Chandra, and Alice would read is in the ratio 4:6:9. Therefore, Bob, Chandra, and Alice read 160, 240, and 360 pages respectively. They would also be reading in the same amount of time because the ratio of pages read was based on the time it takes each of them to read a page. Therefore, the amount of seconds each person reads is 160 * 45, which is 7200.
The least common multiple of 20, 45 and 30 is 2
 
2
 
¢ 3
 
2
 
¢ 5 = 180. Using the
 
LCM, in 180 seconds Alice reads
 
18
 
20 = 9 pages, Chandra reads
 
180
 
30 = 6 pages
 
and Bob reads
 
180
 
45 = 4 pages. Together they read a total of 19 pages in 180
 
seconds. The total number of seconds each reads is
 
760
 
19
 
¢ 180 = 7200.}}
 
 
 
{{AMC8 box|year=2006|num-b=15|num-a=17}}
 

Revision as of 13:01, 11 November 2012

Problem

Problems 14, 15 and 16 involve Mrs. Reed's English assignment.

A Novel Assignment

The students in Mrs. Reed's English class are reading the same 760-page novel. Three friends, Alice, Bob and Chandra, are in the class. Alice reads a page in 20 seconds, Bob reads a page in 45 seconds and Chandra reads a page in 30 seconds.

Before Chandra and Bob start reading, Alice says she would like to team read with them. If they divide the book into three sections so that each reads for the same length of time, how many seconds will each have to read?

$\textbf{(A)}\ 6400\qquad\textbf{(B)}\ 6600\qquad\textbf{(C)}\ 6800\qquad\textbf{(D)}\ 7000\qquad\textbf{(E)}\ 7200$

Solution

(e) The amount of pages Bob, Chandra, and Alice would read is in the ratio 4:6:9. Therefore, Bob, Chandra, and Alice read 160, 240, and 360 pages respectively. They would also be reading in the same amount of time because the ratio of pages read was based on the time it takes each of them to read a page. Therefore, the amount of seconds each person reads is 160 * 45, which is 7200.

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