Question 106747: Mike and Matthew are each responsible for mowing half of their 60 foot by 100 foot rectangular back yard. MIke starts mowing at an outside corner, gradually working his way toward the middle by mowing around the outside edges. If the mower cuts a 3-foot-wide path, during which trip around the yard should Mike stop and Matthew start mowing?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Mike and Matthew are each responsible for mowing half of their 60 foot by 100 foot rectangular back yard. MIke starts mowing at an outside corner, gradually working his way toward the middle by mowing around the outside edges. If the mower cuts a 3-foot-wide path, during which trip around the yard should Mike stop and Matthew start mowing?
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Find the total area: 60 * 100 = 6000 sq/ft
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Half the area = 3000 sq/ft
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Let x = no. of trips by a 3' mower to do 3000 sq/ft (half the lawn
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Area of the unmowed area remaining (each round trip cuts 6' off the edge:
(60-6x) * (100 - 6x) = 3000
:
6000 - 960x + 36x^2 = 3000
Arrange as a quadratic equation:
36x^2 - 960x + 6000 - 3000 = 0
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36x^2 - 960x + 3000 = 0
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Simplify, divide equation by 12:
3x^2 - 80x + 250 = 0
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Using the quadratic formula, the lower value solution:
x = 3.6 trips
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Try to verify this:
Remember that each round he would chop 6' off the lawn dimensions
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if he mowed exactly 3 times 3(6) = 18 ft
The remaining lawn would be:
(60 - 18) * (100 - 18) = 3444 sq/ft remaining, not quite a half done
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If he mowed exactly 4 time; 4(6) = 24 ft
(60 - 24) * (100 - 24) = 2736 sq/ft remaining, over half done
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Between the 3rd and 4th round would be the time for Matthew to take over.
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