Math Problem Statement

Shryia read a 481-page-long book cover to cover in a single session, at a constant rate. After reading for 1.5 hours, she had 403 pages left to read. How fast was Shryia reading? How long did it take her to read the entire book?

Solution

Let's break down the problem step by step:

  1. Total pages in the book: 481 pages.
  2. Pages left after 1.5 hours: 403 pages.

Step 1: Determine how many pages Shryia read in 1.5 hours.

The number of pages Shryia read after 1.5 hours is: 481403=78 pages.481 - 403 = 78 \text{ pages}.

Step 2: Calculate Shryia's reading speed.

Since Shryia read 78 pages in 1.5 hours, her reading speed (in pages per hour) is: Speed=78 pages1.5 hours=52 pages per hour.\text{Speed} = \frac{78 \text{ pages}}{1.5 \text{ hours}} = 52 \text{ pages per hour}.

Step 3: Determine how long it took her to read the entire book.

Now that we know her speed is 52 pages per hour, we can calculate the time it took to read the entire 481-page book: Time=481 pages52 pages per hour9.25 hours.\text{Time} = \frac{481 \text{ pages}}{52 \text{ pages per hour}} \approx 9.25 \text{ hours}.

Answers:

  • Shryia's reading speed: 52 pages per hour.
  • Time taken to read the entire book: 9.25 hours.

Would you like any more details or further clarifications?

Here are 5 additional related questions to deepen your understanding:

  1. How many pages would Shryia read in 3 hours?
  2. If Shryia took a 30-minute break, how would it affect her total reading time?
  3. What if the book had 600 pages—how would that change her total reading time?
  4. How long would it take Shryia to read 150 pages at her constant speed?
  5. If Shryia's speed increased by 10%, how fast would she be reading?

Tip: To calculate time, always remember the formula Time=Total workRate\text{Time} = \frac{\text{Total work}}{\text{Rate}}, whether the work is pages, distance, or another unit.

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Math Problem Analysis

Mathematical Concepts

Algebra
Rates
Linear Equations

Formulas

Speed = Pages read / Time
Time = Total pages / Reading speed

Theorems

Linear relationship between speed, time, and distance (or pages in this case)

Suitable Grade Level

Grades 6-8