Final answer:
Using the linear equation ŷ = 1350 - 1.2x, it is calculated that after 20 hours of work, 1326 acres are left, after 100 hours, 1230 acres are left, and it takes 1125 hours to mow the entire 1345 acres.
Step-by-step explanation:
The student's question involves solving problems using a linear equation, which is a mathematical concept typically found in algebra. The provided equation is ŷ = 1350 - 1.2x, which relates the number of acres left to mow (ŷ) to the number of hours of work (x).
Exercise Answers
- After 20 hours, to find the number of acres left to mow, we substitute x with 20 in the equation: ŷ = 1350 - 1.2(20) = 1350 - 24 = 1326 acres.
- After 100 hours, substituting x with 100 gives us: ŷ = 1350 - 1.2(100) = 1350 - 120 = 1230 acres.
- To find when all lawns are mowed (ŷ = 0), we solve for x: 0 = 1350 - 1.2x, which gives x = 1350 / 1.2 = 1125 hours.
Summary: After 20 hours of work, there are 1326 acres left to mow. After 100 hours, there are 1230 acres remaining. It takes 1125 hours to mow all the lawns.