Math Problem Statement

Suatu proyek perbaikan jalan harus selesai selama 43 hari dengan pekerja sebanyak 17 orang. Setelah 5 hari pelaksanaan, proyek tersebut dihentikan selama x hari karena suatu masalah. Oleh sebab itu, dibutuhkan tambahan pekerja sebanyak 2 orang agar proyek dapat selesai tepat waktu. Jika kemampuan bekerja setiap orang dianggap sama, nilai x adalah ....

Solution

Let's analyze the problem:

The project was originally planned to take 43 days with 17 workers. After 5 days, work stopped for xx 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 xx.

Here are the steps to solve it:

  1. Calculate the total work: The total work needed to complete the project is: Total Work=17×43 (worker-days)\text{Total Work} = 17 \times 43 \text{ (worker-days)}

  2. Work done in the first 5 days: In the first 5 days, 17 workers worked, so: Work Done in 5 Days=17×5\text{Work Done in 5 Days} = 17 \times 5

  3. Work to be completed after 5 days: After 5 days, the remaining work is: Remaining Work=17×4317×5=17×(435)\text{Remaining Work} = 17 \times 43 - 17 \times 5 = 17 \times (43 - 5)

  4. Work after xx days of pause: When the project stops for xx days, no work is done, but the time left to finish the project is reduced by xx. The new workforce is 19 workers (17 original + 2 extra).

  5. Remaining work must be completed in the remaining time: After 5+x5 + x days, 435x43 - 5 - x days remain. In this time, 19 workers will complete the rest of the work. So, the equation for remaining work is: 19×(435x)=17×(435)19 \times (43 - 5 - x) = 17 \times (43 - 5)

  6. Solve the equation: Now, solve this equation to find xx.

Let me calculate the value of xx.The value of xx 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:

  1. What if the number of workers wasn't increased? How would this affect the project timeline?
  2. How many total worker-days were required to complete the project?
  3. If the project had been stopped for 6 days instead, how many additional workers would be needed to finish on time?
  4. What would happen if the number of initial workers was fewer, say 15 workers?
  5. 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