SOLUTION: Two landscapes must mow a rectangular lawn that measures 100 feet by 200 feet. Each wants to mow no more than half of the lawn. The first starts by mowing around the outside of the

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Two landscapes must mow a rectangular lawn that measures 100 feet by 200 feet. Each wants to mow no more than half of the lawn. The first starts by mowing around the outside of the      Log On


   

Question 993841: Two landscapes must mow a rectangular lawn that measures 100 feet by 200 feet. Each wants to mow no more than half of the lawn. The first starts by mowing around the outside of the lawn. How wide a strip must the first landscaper mow on each side of the four sides in order to mow no more than half of the lawn? The mower has a 24 inch cut. Approximate the required number of trips around the lawn.
I have no idea how to set up an equation for this word problem.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Best to try to break the steps into each trip around for the first mower/landscaper.

24 inches is 2 feet.
Trip 1 mows leaves unmowed %28100-2%2A2%29%28200-2%2A2%29
Trip 2 leaves unmowed %28100-2%2A2-2%2A2%29%28200-2%2A2-2%2A2%29
Trip 3 leaves unmowed %28100-2%2A2-2%2A2-2%2A2%29%28200-2%2A2-2%2A2-2%2A2%29
Trip n leaves unmowed %28100-n%2A2%5E2%29%28200-n%2A2%5E2%29, according to the developing pattern.

HALF the lawn's area is 100%2A200%2F2=100%2A100=10000.

How many trips around, n, will leave an unmowed area of 10000?
%28100-n%2A2%5E2%29%28200-n%2A2%5E2%29=10000
and this would hopefully show a solved value for n to be a whole number.