Math Problem Statement

Daniel records the numbers of pages he reads and the amount of hours it takes him. (7.RP.2b) Hours Pages 2 30 4 60 90 6 How many pages does Daniel read per hour? A 15 pages an hour B 25 pages an hour C 30 pages an hour D 60 pages an hour

Solution

To determine how many pages Daniel reads per hour, we first need to identify a constant unit rate from the data provided.

From the table:

  • In 2 hours, Daniel reads 30 pages.
  • In 4 hours, he reads 60 pages.
  • In 6 hours, he reads 90 pages.

Now let's find the rate of pages read per hour:

Pages per hour=PagesHours\text{Pages per hour} = \frac{\text{Pages}}{\text{Hours}}

We can use any of the time intervals, as the rate should be constant. Let's use the first set of data (2 hours, 30 pages):

30 pages2 hours=15 pages per hour\frac{30 \text{ pages}}{2 \text{ hours}} = 15 \text{ pages per hour}

Therefore, Daniel reads 15 pages per hour.

The correct answer is: A) 15 pages an hour

Would you like more details on how this is calculated or have any questions?

Here are 5 related questions to explore:

  1. If Daniel reads for 10 hours, how many pages will he complete?
  2. If Daniel wants to read 120 pages, how many hours will it take him?
  3. What is the unit rate for pages per minute instead of hours?
  4. If Daniel's reading speed improves by 5 pages per hour, how many pages will he read in 4 hours?
  5. If Daniel reads 45 pages in 3 hours, does his reading rate change?

Tip: When solving rate problems, always look for a consistent ratio by dividing quantities of the same units.

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Math Problem Analysis

Mathematical Concepts

Ratio and Proportional Relationships
Unit Rate
Division

Formulas

Pages per hour = Pages / Hours

Theorems

Proportional Relationships

Suitable Grade Level

Grade 7