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Grade 6 Math Problem: Will Marie Finish a 45-Page Chapter in 8 Hours Writing 4 Pages Per Hour?
Mathematics
Grade 6 of Primary School
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. Substitute the values: Total Pages = 4 pages/hour × 8 hours = 32 pages.
2
Step 2: Compare the number of pages Marie can write (32 pages) with the required number of pages (45 pages). Since 32 < 45, Marie cannot write enough pages in 8 hours to complete the chapter.
3
Alternative Step: Calculate the time needed to write 45 pages using Time = Total Pages / Writing Speed. Time = 45 / 4 = 11.25 hours. Since 11.25 > 8, Marie needs more time than she has to finish the chapter.
Knowledge Points Involved
1
Rate-Time-Total Quantity Relationship
A variation of the distance-speed-time formula, where rate (pages per hour) × time (hours) = total quantity (pages written). It is used to calculate total work output when a constant rate and time are known, applied in work-related problems like writing, manufacturing, etc.
2
Whole Number Multiplication
Used here to find the total pages Marie can write by multiplying her writing rate (a whole number) by the available time (a whole number).
3
Comparing Whole Numbers
Used to compare the total pages Marie can write with the required chapter length to determine if she can finish on time.
4
Division of Whole Numbers
Can be used to calculate the time required to complete the total work by dividing the total quantity by the rate, which provides an alternative way to solve the problem.
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