Math Problem Statement

A worker has an average observed time of 15 minutes per cycle for one activity. The worker's performance rating is 97%. An allowance for fatigue is given as 5%, and special allowances are given as 2%. What is the standard time for this activity? (Enter your numbers in minutes)

Solution

To find the standard time for the activity, we use the following formula:

Standard Time=Observed Time×(Performance Rating100)×(1+Allowance Factor)\text{Standard Time} = \text{Observed Time} \times \left( \frac{\text{Performance Rating}}{100} \right) \times \left( 1 + \text{Allowance Factor} \right)

Where:

  • Observed Time = 15 minutes
  • Performance Rating = 97% = 0.97
  • Fatigue Allowance = 5% = 0.05
  • Special Allowances = 2% = 0.02

First, we calculate the total allowance factor:

Allowance Factor=5%+2%=7%=0.07\text{Allowance Factor} = 5\% + 2\% = 7\% = 0.07

Now, we can calculate the standard time:

Standard Time=15×0.97×(1+0.07)\text{Standard Time} = 15 \times 0.97 \times (1 + 0.07) Standard Time=15×0.97×1.07\text{Standard Time} = 15 \times 0.97 \times 1.07 Standard Time=15×1.0389=15.5835 minutes\text{Standard Time} = 15 \times 1.0389 = 15.5835 \text{ minutes}

So, the standard time for the activity is 15.58 minutes.

Would you like more details on the calculation? Let me know if you have any questions.

Here are some related questions for further exploration:

  1. How does the performance rating impact the standard time?
  2. What is the purpose of adding allowances to the observed time?
  3. How would the standard time change if the observed time were different?
  4. How do fatigue and special allowances affect overall productivity?
  5. What is the difference between a performance rating and a normal time?

Tip: Always check the units when performing calculations involving percentages to ensure consistency in the final result.

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Math Problem Analysis

Mathematical Concepts

Time Study
Standard Time Calculation
Percentage Calculations

Formulas

Standard Time = Observed Time × (Performance Rating / 100) × (1 + Allowance Factor)
Allowance Factor = Fatigue Allowance + Special Allowances

Theorems

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Suitable Grade Level

Grades 10-12