Final answer:
Using provided formulas and scale factors, the calculation of areas left to mow after a certain number of hours, total time to mow, and distances on scaled drawings were determined.
Step-by-step explanation:
Problem Solving with Mathematical Equations
To find out how many acres are left to mow after 20 hours, we substitute x = 20 into the equation ŷ = 1350 - 1.2x. This gives us:
ŷ = 1350 - 1.2(20) = 1350 - 24 = 1326 acres left to mow.
After 100 hours of work, the equation becomes:
ŷ = 1350 - 1.2(100) = 1350 - 120 = 1230 acres left to mow.
To mow all the lawns, we have to find the value of x when ŷ = 0:
0 = 1350 - 1.2x
1.2x = 1350
x = 1350 / 1.2 = 1125 hours to mow all lawns.
Understanding Scale Factors and Conversions
The distance on a scale drawing for Calvin's map with a scale factor of 1/800 for an 80 meter distance is calculated as follows:
Scale drawing distance = Actual distance x Scale factor
Scale drawing distance = 80 meters x (1/800) = 0.1 meters or 10 centimeters on the map.