chris cuts half a rectangular lawn, 40m by 30m, by mowing strips of equal width around the perimeter. Jerri cuts the small rectangle left. How wide a stripe does Chris cut so they share the work equally
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To find out how wide a stripe Chris should cut in order to share the work equally with Jerri, we can start by calculating the area of the rectangle.
The area of the rectangular lawn is determined by multiplying its length by its width. In this case, the length is 30 meters and the width is 40 meters, so the area is:
Area = length * width
Area = 30m * 40m
Area = 1200 square meters
Since Chris cuts half of the lawn, he will mow a rectangle with an area equal to half of the total area of the lawn, which is 1200 square meters / 2 = 600 square meters.
The remaining area that Jerri will mow is also 600 square meters since they want to share the work equally.
Jerri's portion forms a smaller rectangle within the original rectangular lawn. Let's say the width of the stripe Chris mows is "x" meters. Jerri's rectangle will have a width of 40 meters minus twice the stripe width (since there are two sides), so the width of Jerri's rectangle becomes (40 - 2x) meters.
Now, we can calculate the area of Jerri's rectangle by multiplying its width by its length:
Area of Jerri's rectangle = length * width
Area of Jerri's rectangle = 30m * (40 - 2x)m
Area of Jerri's rectangle = (1200 - 60x) square meters
Since the area of Jerri's rectangle equals 600 square meters, we can set up the following equation:
1200 - 60x = 600
Now, solve for "x":
1200 - 60x = 600
-60x = 600 - 1200
-60x = -600
x = -600 / -60
x = 10
Therefore, the width of the stripe that Chris should cut so they share the work equally is 10 meters.