SOLUTION: Two young boys, Bob and Tom, are mowing grass one summer as a means of making money to save for their college education. They always split the work and proceeds equally. They have

Question 305090: Two young boys, Bob and Tom, are mowing grass one summer as a means of making money to save for their college education. They always split the work and proceeds equally. They have one lawnmower. They obtain a new job which involves mowing a 40' by 80' rectangular vacant lot. The owner wants it mowed in a collapsing pattern (begin mowing around the outside perimeter, with each pass moving closer to the center of the lot). Bob will mow first, turning the work over to Tom when he has mowed exactly half the area. Bob decides that he will stop at a uniform distance in from the perimeter on all sides, leaving a remaining rectangle for Tom to complete. At what uniform distance (in feet to 2 decimal places) should Bob stop mowing? Solve by creating and solving a quadratic equation. How do you solve this problem I do not understand?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
This problem wants us to find the width of the mown portion that will leave half
the total area of the lawn to be mown
:
40 * 80 = 3200 sq/ft total area of the lot
then
1600 sq/ft = half the area
:
let x = the width of the mown portion
then
(80-2x) by (40-2x) = area of the unmown portion
:
(80-2x) * (40-2x) = 1600
FOIL
3200 - 160x - 80x + 4x^2 = 1600
:
Arrange as a quadratic equation
4x^2 - 240x + 3200 - 1600 = 0
:
4x^2 - 240x + 1600 = 0
Simplify, divide by 4
x^2 - 60x + 400 = 0
:
Will not factor, use the quadratic formula

in this equation a=1; b=-60; c=400

Two solutions

x =
x = 52.36, not a possible solution
and

x =
x = 7.64 ft is the width of the mown portion of lawn
:
:
Check solution by finding the area of the unmown portion (half)
Using a calc: (80-15.28)*(40-15.28) = 1599.88 ~ 1600 sq/ft; confirms solution
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