To tackle this question, let's break down the problem:
Given:
1. Victoria read two novels, each of them is 160 pages long.
2. Her average reading speed of the science fiction novel is 2 pages per hour more than her average reading speed of the historical fiction novel.
3. The average reading speed of the historical fiction novel is represented as [tex]\( x \)[/tex].
We need to interpret the mathematical model provided, [tex]\(\frac{160}{x} + \frac{160}{x + 2}\)[/tex], where [tex]\( x + 2 \)[/tex] appears.
Let's analyze what [tex]\( x + 2 \)[/tex] represents:
- [tex]\( x \)[/tex] is the average reading speed in pages per hour for the historical fiction novel.
- [tex]\( x + 2 \)[/tex] is therefore the rate at which Victoria reads the science fiction novel, because it includes the additional speed of 2 pages per hour.
To verify, let's look at each option:
A. the average reading speed of the historical fiction novel:
- This would be simply [tex]\( x \)[/tex], not [tex]\( x + 2 \)[/tex].
B. the average reading speed of the science fiction novel:
- This correctly describes [tex]\( x + 2 \)[/tex], which accounts for Victoria's reading speed being 2 pages per hour faster than [tex]\( x \)[/tex].
C. the total time taken to read the novels:
- This refers to the expression [tex]\(\frac{160}{x} + \frac{160}{x + 2}\)[/tex], which is the sum of the times taken to read both novels, but not [tex]\( x + 2 \)[/tex] itself.
D. the number of pages of the science fiction novel:
- Both novels are 160 pages, not related to the value [tex]\( x + 2 \)[/tex].
Considering the above reasoning, the correct interpretation of [tex]\( x + 2 \)[/tex] is:
B. the average reading speed of the science fiction novel.
