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Math Help - around a fence

  1. #1
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    around a fence

    Randy & his sister agreed that they would each mow one-half of the lawn. the lawn is a 25'x45' rectangle. the lawn mower cuts a path 2 ft. wide. if randy starts at one corner and mows a path completely around the outside, how many times should he go around to mow one half of the lawn?
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  2. #2
    MHF Contributor Quick's Avatar
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    Quote Originally Posted by blame_canada100 View Post
    Randy & his sister agreed that they would each mow one-half of the lawn. the lawn is a 25'x45' rectangle. the lawn mower cuts a path 2 ft. wide. if randy starts at one corner and mows a path completely around the outside, how many times should he go around to mow one half of the lawn?
    After mowing once there will be a 21'x41' rectangle left to do, in other words, each time he goes around once the dimensions will shrink by 4 feet.

    The area of a 25x45 foot rectangle is 1125, half of that would be 562.5

    Now write out a table...

    Dimensions of Rectangle...................Area

    25x45...........................................11 25
    21x41...........................................86 1
    17x37...........................................62 9


    So he will go around a bit more than 2 times.
    Last edited by Quick; September 11th 2006 at 04:12 PM.
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  3. #3
    dan
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    Quote Originally Posted by Quick View Post
    After mowing once there will be a 23'x43' rectangle left to do, in other words, each time he goes around once the dimensions will shrink by 2 feet.

    The area of a 25x45 foot rectangle is 1125, half of that would be 562.5

    Now write out a table...

    Dimensions of Rectangle...................Area

    25x45...........................................11 25
    23x43...........................................98 9
    21x41...........................................86 1
    19x39...........................................74 1
    17x37...........................................62 9
    15x35...........................................52 5


    So he will go around a bit less than 5 times.
    isn't this some kind of quadradic?? i bet she needs a precise answer...
    dan
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  4. #4
    MHF Contributor Quick's Avatar
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    Quote Originally Posted by dan View Post
    isn't this some kind of quadradic?? i bet she needs a precise answer...
    dan
    You just have to make things complicated

    Although I don't know a formula, I get the answer to be 2.3078703703703703703703703... times around the yard
    Last edited by Quick; September 11th 2006 at 04:13 PM.
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  5. #5
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    Thx! But Whats The Answer?
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  6. #6
    MHF Contributor Quick's Avatar
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    Quote Originally Posted by The Answer View Post
    2.3078703703703703703703703...
    But are you concerned with the method of getting there?
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  7. #7
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Quick View Post
    After mowing once there will be a 23'x43' rectangle left to do, in other words, each time he goes around once the dimensions will shrink by 2 feet.
    Note that if you go around the perimeter mowing a 2 ft. wide path the new dimensions will be less by 4 ft., not 2 ft., because we are taking off 2 ft. from each side of the rectangle. You need to take this change into account.

    -Dan

    SOMEwhere on the forum is a nearly exact copy of the same problem. I can't seem to find it. (I've never gotten the hang of using the search feature on this thing.) Perhaps someone else will have better luck looking for it.
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  8. #8
    MHF Contributor Quick's Avatar
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    Quote Originally Posted by topsquark View Post
    Note that if you go around the perimeter mowing a 2 ft. wide path the new dimensions will be less by 4 ft., not 2 ft., because we are taking off 2 ft. from each side of the rectangle. You need to take this change into account.

    -Dan
    Darn, I missed that. I've changed my posts with the correction.

    PS I've never been able to get the search thing to work
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