Victoria read a 160-page historical fiction novel followed by a science fiction novel of the exact same length. Her average reading speed of the science fiction novel was 2 pages per hour more than her average reading speed of the historical fiction novel.

Victoria models her novel reading marathon with the following expression, where [tex]$x$[/tex] represents her average reading speed of the historical fiction novel.

[tex]\[ \frac{160}{x} + \frac{160}{x+2} \][/tex]

What does [tex]$x+2$[/tex] represent in this situation?

A. The average reading speed of the historical fiction novel
B. The average reading speed of the science fiction novel
C. The total time taken to read the novels
D. The number of pages of the science fiction novel



Answer :

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.