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.