SOLUTION: John and Paul agree to share the work in mowing a rectangular lawn. John agrees to mow half the lawn measuring 30m by 40m by mowing strips of uniform width around the perimeter. Pa

Question 128438: John and Paul agree to share the work in mowing a rectangular lawn. John agrees to mow half the lawn measuring 30m by 40m by mowing strips of uniform width around the perimeter. Paul agrees to mow the small remaining rectangle when John is finished. How wide a strip should John mow to ensure they share the work equally???
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
John and Paul agree to share the work in mowing a rectangular lawn. John agrees to mow half the lawn measuring 30m by 40m by mowing strips of uniform width around the perimeter. Paul agrees to mow the small remaining rectangle when John is finished. How wide a strip should John mow to ensure they share the work equally???
:
Let x = the width of the strip mowed around the perimeter
:
Find the total area of the lawn
30 * 40 = 1200 sq/ft
Then
Half the area = 600 sq/ft
:
Find the value of x using the equation:
(30-2x)(40-2x) = 600
FOIL
1200 - 60x - 80x + 4x^2 = 600
:
Arrange as a quadratic equation:
4x^2 - 140x + 1200 - 600 = 0
:
4x^2 - 140x + 600 = 0
:
Simplify, divide equation by 4
x^2 - 35x + 150 = 0
:
Factor this to:
(x - 5)(x - 30) = 0
:
x = 5 ft is the only solution that is reasonable
:
:
Check the un-mowed center area
(30-10) * (40-10) = 600 sq/ft
:
A 5 ft strip should be mown

RELATED QUESTIONS
Glenn cuts half a rectangular lawn, 40m by 30m, by mowing strips of equal width around... (answered by ankor@dixie-net.com)

quadratic equations-word problem Chris cuts half a rectangular lawn, 40m by 30m, by... (answered by ankor@dixie-net.com)

Glenn cuts half a rectangular lawn, 40m by 30m, by mowing strips of equal width around... (answered by solver91311)

Chris cuts half a rectangle lawn, 40m by 30m, by mowing strips of equal width around the... (answered by checkley75)

John and Sam have a lawn mowing service. At one home, John can mow the lawn by himself in (answered by ikleyn)

Mowing a lawn. Adam can mow a lawn in 40 minutes, while his cousin Victor can mow the... (answered by richwmiller)

Peter can mow a lawn in 40 minutes. John can mow the same lawn in 60 minutes. How long... (answered by ikleyn,josgarithmetic,math_tutor2020,greenestamps)

It takes 3 hours for John to mow the lawn. Linda can mow the same lawn for 5 hours. How... (answered by josmiceli)

When Tim and John work together they can mow their entire lawn in 4 hours and 36 minutes. (answered by josmiceli)