Final answer:
The unit rate for one employee is 50 feet of fence per day. To install 150 feet of fence, a proportion (50 feet/1 employee = 150 feet/x employees) can be set up, revealing that three employees are needed to complete the work in one day.
Step-by-step explanation:
Calculating the Unit Rate and Proportion for Fence Installation
If two employees of Frontier Fence Company can install 100 feet of fence in two days, the unit rate for one employee is calculated by dividing the total feet of fence by the product of the number of days and the number of employees. Therefore, the unit rate for one employee is 50 feet per day (100 feet / (2 employees * 2 days) = 50 feet per employee per day).
Proportion for 150 Feet of Fence
To write a proportion for 150 feet of fence, one can set up a ratio that compares the rate at which one employee can install the fence to the new amount of fence:
(50 feet per day) / (1 employee) = (150 feet) / (x employees)
Calculating the Number of Employees for 150 Feet in One Day
Using the proportion from above and solving for 'x', we find that three employees are needed to install 150 feet of fence in one day. This is because 150 feet divided by the unit rate of 50 feet per day equals 3.