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Compare Proportional Relationships Quick Check

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Question
Use the image and table to answer the question.

An illustration shows a graph labeled Reading Rate. The horizontal axis is labeled hours and ranges from 0 to 6 in increments of 1. The vertical axis is labeled pages and ranges from 0 to 60 in increments of 10. An upward slanting line segment connects points plotted at left parenthesis 0 comma 0 right parenthesis, left parenthesis 1 comma 10 right parenthesis, left parenthesis 2 comma 20 right parenthesis, left parenthesis 3 comma 30 right parenthesis, left parenthesis 4 comma 40 right parenthesis, and left parenthesis 5 comma 50 right parenthesis.

Reading Rate for Student 2
Hours Pages
2 30
3 45
4 60
The reading rate for Student 1 is displayed in the graph and the reading rate for Student 2 is displayed in the table. Which student reads faster and by how much?

(1 point)
Responses

Student 1 reads faster than Student 1 by 5 pages per hour.
Student 1 reads faster than Student 1 by 5 pages per hour.

Student 2 reads faster than Student 1 by 5 pages per hour.
Student 2 reads faster than Student 1 by 5 pages per hour.

Student 2 reads faster than Student 1 by 15 pages per hour.
Student 2 reads faster than Student 1 by 15 pages per hour.

Student 1 reads faster than Student 2 by 10 pages per hour.

1 answer

To compare the reading rates of Student 1 and Student 2, we first need to determine their reading rates, which is calculated as the number of pages read per hour.

For Student 1: From the graph:

  • At 0 hours, 0 pages
  • At 1 hour, 10 pages
  • At 2 hours, 20 pages
  • At 3 hours, 30 pages
  • At 4 hours, 40 pages
  • At 5 hours, 50 pages

The increase in pages is consistent, so we can see that Student 1 reads 10 pages per hour.

For Student 2: From the table:

  • At 2 hours, 30 pages
  • At 3 hours, 45 pages
  • At 4 hours, 60 pages

Let's calculate the reading rate for Student 2:

  • From 2 to 3 hours: 15 pages over 1 hour (45 pages - 30 pages)
  • From 3 to 4 hours: 15 pages over 1 hour (60 pages - 45 pages)

Thus, for Student 2, the reading rate is also consistent, and the average reading rate can be determined by considering the total pages and the total hours (2 to 4 hours):

  • Pages read: 60 pages
  • Time taken: 4 hours - 2 hours = 2 hours
  • Average reading rate = 60 pages / 2 hours = 30 pages per hour.

Comparison:

  • Student 1: 10 pages per hour
  • Student 2: 30 pages per hour

Since Student 2 reads faster, we find out by how much: 30 pages per hour (Student 2) - 10 pages per hour (Student 1) = 20 pages per hour.

Therefore, based on the options provided, none of them state the correct difference of 20 pages per hour, but we can confirm that Student 2 reads faster than Student 1 by 20 pages per hour.