Solving Work Rate Problems: How Many Hours a Day for a 10-Day Job?
Solving Work Rate Problems: How Many Hours a Day for a 10-Day Job?
Imagine a scenario where a worker requires a specific amount of time to complete a job. In this case, we need to determine the number of hours per day a man must work to finish a job in a different time frame. This problem is not only a mathematical exercise but also a real-life application of basic arithmetic. Let's break it down step-by-step and explore the logic behind it.
Problem Description
A man working 8 hours a day can finish a job in 12 days. How many hours a day must he work to complete the same job in 10 days?
Step-by-Step Solution
Step 1: Calculate Total Work in Hours
First, we need to find out the total amount of work required in hours. If the man works 8 hours a day for 12 days, then:
Total work 8 hours/day × 12 days 96 hours
Step 2: Determine the Required Daily Work to Finish in 10 Days
To find out how many hours he needs to work each day to finish the job in 10 days, we divide the total work by the number of days:
Hours per day 96 hours ÷ 10 days 9.6 hours/day
Therefore, the man must work 9.6 hours a day to finish the job in 10 days.
Other Perspectives on the Same Problem
Here are a couple of variations of the same problem and their solutions:
Variation 1: Carpenter's Job
A carpenter working 8.5 hours a day can finish a job in 12 days. How many hours a day must he work to finish the job in 10 days?
Solution: 8.5 hours/day × 12 days 102 hours. Working on the job and completing in 10 days means the carpenter has to work 102/10 10.2 hours a day.
Variation 2: Direct Proportion
It's also possible to solve this problem using a simple proportion method:
8.5 hours/day × 12 days 102 hours. So, he will work 102/10 10.2 hours per day.
Conclusion
This problem demonstrates the principle of work rate, which is a fundamental concept in mathematics. Whether it's a worker completing a task over a longer period or a carpenter finishing a project with a shorter deadline, the same underlying logic applies. Understanding work rates is crucial in various fields, including project management, manufacturing, and any job requiring time-sensitive completion.