Math Problem Statement

mads company states that 4 workers can complete a project in 30 days. how many days will it take for 10 workers to complete the same project?

Solution

To solve this problem, we can use the concept of "work" in terms of worker-days, which assumes that the total amount of work is constant.

Step 1: Calculate the total amount of work in worker-days.
If 4 workers can complete the project in 30 days, the total amount of work is:

Total work=4workers×30days=120worker-days\text{Total work} = 4 \, \text{workers} \times 30 \, \text{days} = 120 \, \text{worker-days}

Step 2: Determine how many days it will take for 10 workers to complete the same amount of work.
If the total work is 120 worker-days, and now we have 10 workers, we can find how many days it will take by dividing the total work by the number of workers:

Time required=Total workNumber of workers=120worker-days10workers=12days\text{Time required} = \frac{\text{Total work}}{\text{Number of workers}} = \frac{120 \, \text{worker-days}}{10 \, \text{workers}} = 12 \, \text{days}

So, it will take 10 workers 12 days to complete the project.

Would you like a more detailed breakdown or have any follow-up questions?

Additional Related Questions:

  1. If 8 workers are hired instead of 10, how many days would it take to finish the project?
  2. How would the time change if the number of workers is doubled?
  3. What if only 2 workers were available for the project? How many days would it take?
  4. How many workers would be needed to finish the project in just 6 days?
  5. Can you calculate the total number of worker-days needed if the project required 60 days with 6 workers?

Tip: Always keep in mind that when the number of workers increases, the time taken decreases proportionally, assuming the work rate remains constant.

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Math Problem Analysis

Mathematical Concepts

Work and Time
Proportional Relationships
Basic Algebra

Formulas

Total work = Workers × Days
Time required = Total work / Workers

Theorems

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Suitable Grade Level

Grades 6-8