Final answer:
A line worker who installs 16 insulators in 18 3/4 hours works at a rate of 0.8533 insulators per hour. At this rate, the worker should be able to install approximately 24 insulators in 28 1/8 hours.
Step-by-step explanation:
To determine how many insulators a line worker can install in 28 1/8 hours, we need to calculate the worker's rate of installing insulators. The worker installs 16 insulators in 18 3/4 hours, so first, we convert 18 3/4 hours to a decimal, which is 18.75 hours. Then, we divide the number of insulators by the number of hours to find the rate: 16 insulators/18.75 hours = 0.8533 insulators per hour.
Now, to find out how many insulators can be installed in 28 1/8 hours, we convert 28 1/8 hours to a decimal, which is 28.125 hours. We then multiply this time by the insulator installation rate: 28.125 hours * 0.8533 insulators per hour. This results in a product of 23.9984, which we can round to 24 insulators that the worker should be able to install in 28 1/8 hours.
This calculation allows us to create a proportion based on the worker's rate of installing insulators over time, which we can then use to estimate the number of insulators installed over a different duration.