A clerk processes 62 invoices in 4 hours. How many invoices can the clerk process by working at this rate for 40 hours per week for 6 weeks?
The correct answer and explanation is:
Correct Answer: 3,720 invoices
Explanation:
To determine how many invoices a clerk can process over 6 weeks, begin by finding the clerk’s rate of processing and then multiply that rate by the total number of hours worked in 6 weeks.
Step 1: Find the rate of processing per hour
The clerk processes 62 invoices in 4 hours: Invoices per hour=624=15.5 invoices per hour\text{Invoices per hour} = \frac{62}{4} = 15.5 \text{ invoices per hour}
Step 2: Find total hours worked in 6 weeks
The clerk works 40 hours per week: Total hours in 6 weeks=40 hours/week×6 weeks=240 hours\text{Total hours in 6 weeks} = 40 \text{ hours/week} \times 6 \text{ weeks} = 240 \text{ hours}
Step 3: Calculate total invoices processed
Now multiply the rate of 15.5 invoices per hour by the total hours: 15.5 invoices/hour×240 hours=3,720 invoices15.5 \text{ invoices/hour} \times 240 \text{ hours} = 3,720 \text{ invoices}
Final Answer: 3,720 invoices
Conclusion:
This problem involves a basic application of unit rate and proportional reasoning. First, divide to find the rate of work per hour, then use multiplication to scale up that rate to a longer time frame. It is important to keep units consistent and to multiply properly across them. This method works for many similar problems involving production rates, work hours, and output calculations.