To determine how long it will take the photocopy machine to make 36 copies of a 324-page document, we need to follow a series of steps.
1. Calculate the total number of pages to be copied:
- Each document consists of 324 pages.
- The number of copies needed is 36.
- Therefore, the total number of pages to be copied is:
[tex]\[
36 \text{ copies} \times 324 \text{ pages per copy} = 11664 \text{ pages}
\][/tex]
2. Determine the total time required to copy these pages:
- The machine's copying speed is 24 pages per minute.
- To find the total time (in minutes) needed to copy 11664 pages, we use the following calculation:
[tex]\[
\frac{11664 \text{ pages}}{24 \text{ pages per minute}} = 486 \text{ minutes}
\][/tex]
3. Convert the total copying time from minutes to hours and minutes:
- There are 60 minutes in an hour.
- To convert 486 minutes into hours and minutes, we perform the following division:
[tex]\[
486 \text{ minutes} \div 60 \text{ minutes per hour} = 8 \text{ hours and } 6 \text{ minutes}
\][/tex]
- This division gives us 8 hours and a remainder of 6 minutes.
Therefore, the photocopy machine will take 8 hours and 6 minutes to make 36 copies of a 324-page document.
Now, we compare this result with the given choices:
- A. 13 hours 30 minutes
- B. 10 hours 24 minutes
- C. 8 hours 6 minutes
- D. 3 hours 36 minutes
The correct answer is:
- C. 8 hours 6 minutes
