Math Problem Statement

Leo reads 10 pages in 1/3 hour. What is the unit rate for pages per hour? For hours per page?

Solution

To solve this, we need to determine two unit rates:

  1. Pages per hour:
    • Leo reads 10 pages in 13\frac{1}{3} hour.
    • To find the number of pages he reads in 1 hour, divide 10 pages by 13\frac{1}{3} hour:

Pages per hour=10pages13hour=10×3=30pages per hour\text{Pages per hour} = \frac{10 \, \text{pages}}{\frac{1}{3} \, \text{hour}} = 10 \times 3 = 30 \, \text{pages per hour}

  1. Hours per page:
    • To find the time Leo spends on 1 page, divide 13\frac{1}{3} hour by 10 pages:

Hours per page=13hour10pages=130hours per page\text{Hours per page} = \frac{\frac{1}{3} \, \text{hour}}{10 \, \text{pages}} = \frac{1}{30} \, \text{hours per page}

Final Answers:

  • Pages per hour: 30 pages per hour
  • Hours per page: 130\frac{1}{30} hours per page

Would you like more details or clarifications on any part of this? Here are some related questions:

  1. If Leo reads for 2 hours, how many pages will he have read?
  2. How long will it take Leo to read 90 pages?
  3. What is the time in minutes per page?
  4. If Leo speeds up and reads 40 pages per hour, what is his new hours-per-page rate?
  5. How many pages does Leo read in 45 minutes?

Tip: Unit rates simplify complex ratios into an easy-to-understand form, useful for making comparisons or predictions!

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Math Problem Analysis

Mathematical Concepts

Unit Rate
Ratios
Proportions

Formulas

Pages per hour = Total pages / Time taken in hours
Hours per page = Time taken in hours / Total pages

Theorems

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Suitable Grade Level

Grades 5-6