A compositor takes 1 hour 45 minutes to compose 24 pages of a book. How long will he take to compose 64 pages?

Hint: For composing 1 page, time taken = [tex]\frac{7}{4 \times 24}[/tex] hours.
For composing 64 pages, time taken = [tex]\frac{7 \times 64}{4 \times 24}[/tex] hours.

The compositor will take approximately 4 hours and 40 minutes to compose 64 pages. This is calculated by first determining the time taken to compose one page and then multiplying that by 64. The calculations show that for 64 pages, the total time is 4.67 hours.
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Answered by Anonymous | 2025-07-04

To determine how long it will take for a compositor to compose 64 pages, we can follow a step-by-step approach.
First, let's understand the given hint that helps break down the task of calculating the time taken per page.

Time taken to compose 1 page:
The compositor takes 1 hour and 45 minutes to compose 24 pages, which equates to a total of 105 minutes (since 1 hour = 60 minutes, thus 1 hour 45 minutes = 60 + 45).
To find out the time taken for 1 page, we divide the total time by the number of pages composed:
Time per page = 24 pages 105 minutes ​
This simplifies to approximately 4.375 minutes per page.

Time taken to compose 64 pages:
To find the time taken to compose 64 pages, we multiply the time per page by 64:
Total time for 64 pages = 4.375 minutes per page × 64 pages
Simplifying this gives:
Total time for 64 pages = 280 minutes

Converting minutes back to hours and minutes:
Since there are 60 minutes in an hour, we convert 280 minutes into hours and minutes:
Hours = 60 280 ​ = 4 hours and 40 minutes


Therefore, the compositor will take 4 hours and 40 minutes to compose 64 pages.
This calculation shows how we utilize unitary methods (finding time per single unit and then scaling up) to solve practical problems efficiently.

Answered by LiamAlexanderSmith | 2025-07-06