Final answer:
To find out how many acres are left to mow and the total time needed to mow all of the lawns, the provided equation ŷ = 1350 - 1.2x is used. After 20 hours, 1326 acres remain, after 100 hours, 1230 acres remain, and it takes 1125 hours to mow all the lawns.
Step-by-step explanation:
The student's question involves calculating the total area of grass being cut after a given amount of time using the provided equation. To determine the area remaining after a certain number of hours of work, the equation ŷ = 1350 - 1.2x must be used, where ŷ represents the acres left and x represents the hours of work.
Exercise 31: Acres left after 20 hours
Plugging in 20 hours into the equation:
ŷ = 1350 - 1.2(20)
ŷ = 1350 - 24
ŷ = 1326 acres
Exercise 32: Acres left after 100 hours
Plugging in 100 hours into the equation:
ŷ = 1350 - 1.2(100)
ŷ = 1350 - 120
ŷ = 1230 acres
Exercise 33: Hours to mow all the lawns
Setting the equation to ŷ = 0 to find out when all the lawns are mowed:
0 = 1350 - 1.2x
1.2x = 1350
x = 1350 / 1.2
x = 1125 hours