Kyoko is reading a book by her favorite author. She read the first 20 pages in One-half of an hour. Reading at the same pace, Kyoko wants to determine if she’ll have enough time to finish the book before she has to go to bed.

Question

Reading Time
On a coordinate plane, a graph titled Reading Time has number of hours on the x-axis, and number of pages on the y-axis. A straight line goes through (0, 0), (0.5, 20), and (2, 80).

According to the graph, which statement must be true?
It will take her 2 hours to read 60 pages.
It will take her 3 hours to read 120 pages.
It will take her 4 hours to read 180 pages.
It will take her 5 hours to read 210 pages.

Answer 1

To analyze the information given, we can determine Kyoko's reading rate from the graph.

1. Kyoko reads 20 pages in 0.5 hours. To find her reading rate (pages per hour), we can calculate: \[ \text{Reading rate} = \frac{20 \text{ pages}}{0.5 \text{ hours}} = 40 \text{ pages per hour} \]

Using this reading rate, we can find out how long it will take her to read different numbers of pages as per the options provided:

1. 60 pages: \[ \text{Time} = \frac{60 \text{ pages}}{40 \text{ pages per hour}} = 1.5 \text{ hours} \]

2. 120 pages: \[ \text{Time} = \frac{120 \text{ pages}}{40 \text{ pages per hour}} = 3 \text{ hours} \]

3. 180 pages: \[ \text{Time} = \frac{180 \text{ pages}}{40 \text{ pages per hour}} = 4.5 \text{ hours} \]

4. 210 pages: \[ \text{Time} = \frac{210 \text{ pages}}{40 \text{ pages per hour}} = 5.25 \text{ hours} \]

Now, comparing the calculated reading times with the options given:

• According to the calculations, it will take her 3 hours to read 120 pages, which matches one of the statements provided.

Thus, the statement that must be true is: It will take her 3 hours to read 120 pages.