Machine Bottle Filling Rate Calculation
This problem requires calculating the rate of milk bottles a machine can fill and then determining the output for a different time duration.
Calculate the Filling Rate
First, determine the machine's filling rate in bottles per minute.
- Bottles filled: 120
- Time taken: 6 minutes
- The rate is calculated as: $\text{Rate} = \frac{\text{Number of Bottles}}{\text{Time Taken}}$
- Rate = $\frac{120 \text{ bottles}}{6 \text{ minutes}}$
- Rate = 20 bottles per minute
Calculate Bottles Filled in 14 Minutes
Next, use the established rate to find out how many bottles are filled in 14 minutes.
- Filling Rate: 20 bottles per minute
- New Time Duration: 14 minutes
- Total Bottles = Rate $\times$ New Time Duration
- Total Bottles = $20 \frac{\text{bottles}}{\text{minute}} \times 14 \text{ minutes}$
- Total Bottles = 280 bottles
Result
Therefore, the machine can fill 280 milk bottles in 14 minutes.
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