Difference between revisions of "2006 AMC 8 Problems/Problem 14"

(Created page with "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...")
 
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==Problem==
 
Problems 14, 15 and 16 involve Mrs. Reed's English assignment.  
 
Problems 14, 15 and 16 involve Mrs. Reed's English assignment.  
  
 
A Novel 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.  
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The students in Mrs. Reed's English class are reading the same <math>760</math>-page novel. Three friends, Alice, Bob and Chandra, are in the class. Alice reads a page in 20 seconds, Bob reads a page in <math>45</math> seconds and Chandra reads a page in <math>30</math> seconds.  
  
 
If Bob and Chandra both read the whole book, Bob will spend how many more seconds reading than Chandra?  
 
If Bob and Chandra both read the whole book, Bob will spend how many more seconds reading than Chandra?  
  
 
<math> \textbf{(A)}\ 7,600\qquad\textbf{(B)}\ 11,400\qquad\textbf{(C)}\ 12,500\qquad\textbf{(D)}\ 15,200\qquad\textbf{(E)}\ 22,800 </math>
 
<math> \textbf{(A)}\ 7,600\qquad\textbf{(B)}\ 11,400\qquad\textbf{(C)}\ 12,500\qquad\textbf{(D)}\ 15,200\qquad\textbf{(E)}\ 22,800 </math>
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==Solution==
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The information is the same for Problems 14,15, and 16. Therefore, we shall only use the information we need. All we need for this problem is that there's 760 pages, Bob reads a page in 45 seconds and Chandra reads a page in 30 seconds. A lot of people will find how long it takes Bob to read the book, how long it takes Chandra to read the book, and then find the seconds. However, if we just set up the expression, we can find an easier way.
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<math>760\cdot45 - 760\cdot30 = 760(45-30) = 760(15) = \boxed{\textbf(B)11,400}</math>

Revision as of 12:16, 20 November 2011

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.

If Bob and Chandra both read the whole book, Bob will spend how many more seconds reading than Chandra?

$\textbf{(A)}\ 7,600\qquad\textbf{(B)}\ 11,400\qquad\textbf{(C)}\ 12,500\qquad\textbf{(D)}\ 15,200\qquad\textbf{(E)}\ 22,800$

Solution

The information is the same for Problems 14,15, and 16. Therefore, we shall only use the information we need. All we need for this problem is that there's 760 pages, Bob reads a page in 45 seconds and Chandra reads a page in 30 seconds. A lot of people will find how long it takes Bob to read the book, how long it takes Chandra to read the book, and then find the seconds. However, if we just set up the expression, we can find an easier way.

$760\cdot45 - 760\cdot30 = 760(45-30) = 760(15) = \boxed{\textbf(B)11,400}$

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