15 Taxpayer Agents that work on average 5 hours per day can complete 40 cases in 10 days. If none of the circumstances change, and taxpayer agents of the same efficiency are used in the cases completed, how long would it take 10 Taxpayer Agents to complete 10 cases if they work 10 hours a day?
Answer (2)
It takes 10 taxpayer agents approximately 1.875 days to complete 10 cases if they work 10 hours a day. This is calculated based on the total agent-hours required and their daily working hours. The efficient use of agent-hours allows us to estimate task completion time accurately.
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Calculate the total work done by the 15 agents: 15 × 5 × 10 = 750 agent-hours.
Determine the work rate per case: 40 750 = 18.75 agent-hours/case.
Calculate the total agent-hours required for 10 cases: 10 × 18.75 = 187.5 agent-hours.
Calculate the number of days required for 10 agents working 10 hours/day: 10 × 10 187.5 = 1.875 days. The answer is 1.875 .
Explanation
Problem Analysis Let's analyze the problem. We are given that 15 taxpayer agents working 5 hours a day can complete 40 cases in 10 days. We need to find out how long it would take 10 taxpayer agents working 10 hours a day to complete 10 cases, assuming the same efficiency.
Total Work Done First, we calculate the total work done by the 15 agents. This is given by the number of agents multiplied by the number of hours they work per day and the number of days they work: 15 agents × 5 hours/day × 10 days = 750 agent-hours This means 750 agent-hours are required to complete 40 cases.
Work Rate Per Case Next, we find the work rate per case. This is the total agent-hours divided by the number of cases completed: 40 cases 750 agent-hours = 18.75 agent-hours/case So, it takes 18.75 agent-hours to complete one case.
Total Agent-Hours Required Now, we calculate the total agent-hours required to complete 10 cases: 10 cases × 18.75 agent-hours/case = 187.5 agent-hours Therefore, 187.5 agent-hours are needed to complete 10 cases.
Total Hours Worked Per Day We calculate the total hours worked per day by the 10 agents: 10 agents × 10 hours/day = 100 agent-hours/day So, 10 agents working 10 hours a day contribute 100 agent-hours per day.
Number of Days Required Finally, we determine the number of days required to complete 10 cases by dividing the total agent-hours required by the total agent-hours per day: 100 agent-hours/day 187.5 agent-hours = 1.875 days Rounding to two decimal places, we get 1.88 days.
Final Answer Therefore, it would take 10 Taxpayer Agents 1.875 days (approximately 1.88 days) to complete 10 cases if they work 10 hours a day.
Examples
Understanding work rates is crucial in many real-world scenarios. For example, if you're managing a construction project, knowing how quickly a team can complete a task helps you estimate project timelines and allocate resources effectively. Similarly, in manufacturing, understanding the production rate of a machine helps optimize production schedules and meet customer demands. These calculations ensure efficient operations and prevent costly delays.
