Firm A operates 16 hours each day, producing 80 parts per hour. If productivity were increased by 20%, how many hours would the plant have to work to produce 1000 parts?

Let's solve this step by step:

1. **Current production rate**:  
   Firm A operates for 16 hours a day and produces 80 parts per hour. So, the total daily production is:
   \[
   80 \, \text{parts/hour} \times 16 \, \text{hours} = 1280 \, \text{parts/day}.
   \]

2. **Productivity increase**:  
   A 20% increase in productivity means the new production rate is:
   \[
   80 \, \text{parts/hour} + 0.20 \times 80 \, \text{parts/hour} = 80 \, \text{parts/hour} + 16 \, \text{parts/hour} = 96 \, \text{parts/hour}.
   \]

3. **New production goal**:  
   The goal is to produce 1000 parts. To find out how many hours it will take to produce 1000 parts at the new rate of 96 parts/hour, we use the formula:
   \[
   \text{Time} = \frac{\text{Total parts}}{\text{Parts per hour}} = \frac{1000}{96} \approx 10.42 \, \text{hours}.
   \]

Thus, **Firm A would have to work approximately 10.42 hours** to produce 1000 parts with the 20% increase in productivity.

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Would you like more details on this, or have any questions?

Here are 5 related questions you might explore:
1. How many parts could Firm A produce in 24 hours with the increased productivity?
2. What would happen if productivity increased by 30% instead of 20%?
3. How many hours would it take to produce 2000 parts at the new rate?
4. What would be the daily production if Firm A operated for 12 hours instead of 16?
5. How much time would be saved by the 20% productivity increase to produce 1280 parts?

**Tip**: Always check how increases in productivity affect both the rate and total output to optimize production plans.

Learn how to calculate the time required for Firm A to produce 1000 parts after increasing productivity by 20%. This problem involves key mathematical concepts such as rate calculation, percentage increase, and time estimation. Suitable for students in Grades 8-10.

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