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???
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Let x = the width of the strip mowed around the perimeter
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Find the total area of the lawn
30 * 40 = 1200 sq/ft
Then
Half the area = 600 sq/ft
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Find the value of x using the equation:
(30-2x)(40-2x) = 600
FOIL
1200 - 60x - 80x + 4x^2 = 600
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Arrange as a quadratic equation:
4x^2 - 140x + 1200 - 600 = 0
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4x^2 - 140x + 600 = 0
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Simplify, divide equation by 4
x^2 - 35x + 150 = 0
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Factor this to:
(x - 5)(x - 30) = 0
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x = 5 ft is the only solution that is reasonable
:
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Check the un-mowed center area
(30-10) * (40-10) = 600 sq/ft
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A 5 ft strip should be mown
