To solve this problem, we can break it down into a series of logical steps:
1. Find the rate of bottle production per hour:
- We know the machine makes 60 bottles in 11 hours. To find the production rate per hour, we divide the number of bottles by the number of hours.
[tex]\[
\text{Rate per hour} = \frac{60 \text{ bottles}}{11 \text{ hours}} \approx 5.454545454545454 \text{ bottles per hour}
\][/tex]
This tells us how many bottles the machine produces in one hour.
2. Calculate the number of bottles produced in 16 hours:
- Once we have the rate of production per hour, we can multiply this rate by the number of hours we are interested in (16 hours) to find out how many bottles are produced in that time period.
[tex]\[
\text{Bottles in 16 hours} = \text{Rate per hour} \times 16 \text{ hours} \approx 5.454545454545454 \times 16 \approx 87.27272727272727 \text{ bottles}
\][/tex]
Therefore, the machine will produce approximately 87.27 bottles in 16 hours.
