If 10 agents working 5 hours a day complete 40 cases in 10 days, how long would it take 10 agents working 10 hours a day to complete 10 cases?
Answer (2)
It takes 1.25 days for 10 agents working 10 hours a day to complete 10 cases. This calculation is based on understanding the total work done in agent-hours from a previous scenario. We figured out the needed agent-hours and how quickly the team could work to find the time required.
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Set up a proportion relating agents, hours, days, and cases: C 1 A 1 ". H 1 ". D 1 = C 2 A 2 ". H 2 ". D 2 .
Plug in the given values: 40 10".5".10 = 10 10".10". D 2 .
Simplify the equation: 12.5 = 10 D 2 .
Solve for D 2 : D 2 = 1.25 . The final answer is 1.25 .
Explanation
Problem Analysis Let's analyze the problem. We are given that 10 agents working 5 hours a day complete 40 cases in 10 days. We need to find out how many days it would take for 10 agents working 10 hours a day to complete 10 cases. We can set up a proportion to solve this problem.
Setting up the Proportion Let A be the number of agents, H be the number of hours per day, C be the number of cases, and D be the number of days. We can assume that the amount of work done is proportional to the number of agents, the number of hours per day, and the number of days. It is also inversely proportional to the number of cases. Therefore, we can write the following equation: C 1 A 1 ⋅ H 1 ". D 1 = C 2 A 2 ⋅ H 2 ⋅ D 2
Plugging in the Values In the first scenario, we have A 1 = 10 , H 1 = 5 , D 1 = 10 , and C 1 = 40 . In the second scenario, we have A 2 = 10 , H 2 = 10 , C 2 = 10 , and we want to find D 2 . Plugging these values into the equation, we get: 40 10 ⋅ 5 ⋅ 10 = 10 10 ⋅ 10 ⋅ D 2
Solving for D2 Now, we can simplify the equation and solve for D 2 :
40 500 = 10 100 D 2 12.5 = 10 D 2 D 2 = 10 12.5 D 2 = 1.25
Final Answer Therefore, it would take 1.25 days for 10 agents working 10 hours a day to complete 10 cases.
Examples
Understanding work rate problems like this one can help in project management. For example, if a team of developers can complete a certain number of features in a sprint, you can use similar calculations to estimate how long it will take a different team, or the same team working different hours, to complete a different number of features. This helps in planning timelines and allocating resources effectively. The key is to understand the relationship between the number of workers, the time they spend, and the amount of work they accomplish.
