Math Problem Statement
Solution
Let's analyze the problem:
The project was originally planned to take 43 days with 17 workers. After 5 days, work stopped for days due to an issue. To make up for lost time and still finish the project on time, 2 more workers are added. We need to find the value of .
Here are the steps to solve it:
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Calculate the total work: The total work needed to complete the project is:
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Work done in the first 5 days: In the first 5 days, 17 workers worked, so:
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Work to be completed after 5 days: After 5 days, the remaining work is:
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Work after days of pause: When the project stops for days, no work is done, but the time left to finish the project is reduced by . The new workforce is 19 workers (17 original + 2 extra).
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Remaining work must be completed in the remaining time: After days, days remain. In this time, 19 workers will complete the rest of the work. So, the equation for remaining work is:
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Solve the equation: Now, solve this equation to find .
Let me calculate the value of .The value of is 4. This means the project was stopped for 4 days due to the issue.
Would you like further clarification on any part of the solution? Here are some related questions to explore:
- What if the number of workers wasn't increased? How would this affect the project timeline?
- How many total worker-days were required to complete the project?
- If the project had been stopped for 6 days instead, how many additional workers would be needed to finish on time?
- What would happen if the number of initial workers was fewer, say 15 workers?
- How would the formula change if the time stopped varied throughout the project?
Tip: For problems involving work and time, always consider the total work in terms of worker-days and how changes in workers or time affect completion.
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Math Problem Analysis
Mathematical Concepts
Work and Time
Algebra
Formulas
Total Work = Number of workers × Total days
Remaining Work = Total Work - Work Done
Remaining Work = New workforce × Remaining days
Theorems
Basic Work Formula (Work = Workers × Time)
Suitable Grade Level
Grades 9-12
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