Final answer:
For the paving question, if 130 miles are left, the crew has worked for 8 days. After 13 days, 85 miles remain unpaved. In the landscaping scenario, 1326 acres remain after 20 hours, 1230 acres after 100 hours, and it would take 1125 hours to mow all 1350 acres.
Step-by-step explanation:
The questions you're asking relate to the application of linear functions to real-world problems. Specifically, using a function to describe the remaining task (paving a road or mowing a lawn) as it relates to the effort put in (days of work or hours of mowing).
Question about road paving:
If 130 miles of the road is left to be paved, we use the formula L(D) = 202 - 9D to find out how many days have been spent paving. Substituting 130 for L(D), we get 130 = 202 - 9D. Solving for D gives us D = (202 - 130) / 9. So, the crew has been paving for 8 days.
To find out how many miles are left after 13 days, we substitute D with 13 in the equation, which gives us L(13) = 202 - 9(13) = 202 - 117 = 85 miles left to pave.
Question about mowing acres:
For the landscaping problem, the equation given is ÿ = 1350 - 1.2x. To find the acres left to mow after 20 hours, substitute x with 20, giving ÿ = 1350 - 24 = 1326 acres left. After 100 hours, ÿ = 1350 - 120 = 1230 acres left. For ÿ to be 0, which means all lawns have been mowed, we need to solve 1350 - 1.2x = 0, which will lead to x = 1350 / 1.2, meaning it takes 1125 hours to mow all the lawns.