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 417627: 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.

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
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.
:
Find the area of the yard: 40 * 80 = 3200 sq/ft
then
1600 sq/ft = half the area
:
Let x = the width of the swath around the un-mown portion
This will subtract 2x the each of the overall dimensions
Un-mown rectangle will be (40-2x) by (80-2x)
:
The area equation
(40-2x)*(80-2x) = 1600
FOIL
3200 - 80x - 160x + 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
This looks like it should factor but it doesn't, use the quadratic formula

In this problem a=1; b=-60; c=400

Two solutions

x =
x = 52.36 ft, not possible
and

x =
x = 7.64 ft is the width of the mown area, when he has mown half the yard
;
:
We can confirm this by finding the area of the remaining area
(40-2(7.64)) * (80-2(7.64)) =
(40-15.28) * (80-15.28) =
27.72 * 64.72 = 1599.88 ~ 1600 sq/ft
:
:
Did this all makes sense to you??
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