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Can Marie Write a 45-Page Chapter in 8 Hours at 4 Pages Per Hour? Math Problem
Mathematics
Grade 6
Question Content
Marie has 8 hours to write a 45-page chapter for her book. Marie writes at a constant speed of 4 pages per hour. Will Marie complete the chapter in time? Explain.
Correct Answer
No, Marie will not complete the chapter in time.
Detailed Solution Steps
1
Step 1: Calculate the total number of pages Marie can write in 8 hours using the formula: Total Pages = Writing Speed × Time
2
Step 2: Substitute the given values: Total Pages = 4 pages/hour × 8 hours = 32 pages
3
Step 3: Compare the total pages Marie can write (32 pages) to the required chapter length (45 pages). Since 32 < 45, Marie cannot write enough pages in 8 hours.
4
Step 4: Alternative method: Calculate the time needed to write 45 pages: Time = Total Pages / Writing Speed = 45 / 4 = 11.25 hours. Since 11.25 > 8, Marie needs more time than she has to complete the chapter.
Knowledge Points Involved
1
Work Rate Calculation
Work rate problems use the formula: Total Work = Rate × Time, where work can be measured in units like pages, items produced, etc. It is used to determine how much work can be completed in a given time, or how much time is needed for a given amount of work.
2
Unit Rate Application
A unit rate (like 4 pages per hour) represents the amount of work done per unit time. It is multiplied by total time to find total work, or used to divide total work to find required time.
3
Inequality Comparison for Real-World Decisions
This involves comparing a calculated possible output (pages Marie can write) to a required output (45 pages) using inequalities to make a real-world decision about whether a task can be completed.
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