Math Problem Statement

it 10 workers can complete a job in 24 days, how many workers are required to complete the same job in 18 days?

Solution

To solve this, we can use the concept of "work done" which is a product of the number of workers and the number of days. Since the total work remains constant, we can set up a proportion:

Workers×Days=Constant Work\text{Workers} \times \text{Days} = \text{Constant Work}

Given that 10 workers can complete the job in 24 days, the total work is:

10×24=240worker-days10 \times 24 = 240 \, \text{worker-days}

Let xx be the number of workers required to complete the job in 18 days. The total work must still equal 240 worker-days, so:

x×18=240x \times 18 = 240

Solving for xx:

x=24018=13.33x = \frac{240}{18} = 13.33

Since the number of workers must be a whole number, we round up to the nearest whole number, so:

x=14workersx = 14 \, \text{workers}

Thus, 14 workers are required to complete the job in 18 days.

Would you like more details or have any questions?

Here are 5 related questions for you to consider:

  1. If 12 workers can complete a job in 30 days, how many workers are needed to finish it in 15 days?
  2. If a job requires 20 worker-days, how long will it take 4 workers to complete the job?
  3. How many days will 16 workers take to complete a job if 8 workers can do it in 12 days?
  4. If 6 workers can finish a task in 10 days, how many workers are required to finish it in 5 days?
  5. What is the relationship between workers and time in terms of efficiency?

Tip: Always consider rounding up when calculating workers, since a fraction of a worker isn't practical.

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Math Problem Analysis

Mathematical Concepts

Proportions
Work-Efficiency Relationship
Algebra

Formulas

Workers × Days = Constant Work
x × 18 = 240

Theorems

Direct Proportionality between Workers and Days for Constant Work

Suitable Grade Level

Grades 6-8