Points to Remember:
- Rate of printing: Determine the printing speed of A and B in pages per minute.
- Time comparison: Calculate the time A takes to print 60 pages.
- Total pages: Use the time calculated and B’s printing speed to find the number of pages B prints.
Introduction:
This is a rate and time problem involving two individuals, A and B, printing documents at different speeds. We are given the rate at which A prints pages and the rate at which B prints pages. The question requires us to calculate the number of pages B will print in the same time it takes A to print a specific number of pages. This involves converting different units of time (hours and minutes) to a common unit for consistent calculation.
Body:
1. Determining A’s printing rate:
- A prints 30 pages in 2 hours (120 minutes).
- A’s printing rate is 30 pages / 120 minutes = 0.25 pages/minute.
2. Calculating the time A takes to print 60 pages:
- A’s printing rate is 0.25 pages/minute.
- To print 60 pages, A will take 60 pages / 0.25 pages/minute = 240 minutes.
3. Determining B’s printing rate:
- B takes 5 minutes to print 1 page.
- B’s printing rate is 1 page / 5 minutes = 0.2 pages/minute.
4. Calculating the number of pages B prints in 240 minutes:
- B’s printing rate is 0.2 pages/minute.
- In 240 minutes, B will print 0.2 pages/minute * 240 minutes = 48 pages.
Conclusion:
In summary, A prints at a rate of 0.25 pages per minute, while B prints at a rate of 0.2 pages per minute. It takes A 240 minutes to print 60 pages. Therefore, in the same 240 minutes, B will print 48 pages. This problem highlights the importance of understanding and converting units of measurement to solve problems involving rates and time efficiently. No policy recommendations or best practices are applicable in this purely mathematical context. The solution demonstrates a clear and logical approach to solving rate-related problems, emphasizing the importance of accurate calculations and unit consistency.