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A rectangular pasture has fence posts along every side at 15-foot

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A rectangular pasture has fence posts along every side at 15-foot [#permalink]

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New post 10 Aug 2017, 21:08
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A rectangular pasture has fence posts along every side at 15-foot intervals. If there are 6 fence posts along the length of the pasture and the perimeter of the pasture is 240 feet, how many fence posts would surround this pasture if the width were doubled? (Assume that the space taken up by the fence posts is negligible.)

A) 14
B) 16
C) 20
D) 22
E) 24
[Reveal] Spoiler: OA

Last edited by Bunuel on 10 Aug 2017, 21:50, edited 1 time in total.
Renamed the topic, edited the question and added the OA.

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Re: A rectangular pasture has fence posts along every side at 15-foot [#permalink]

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New post 10 Aug 2017, 21:24
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response D = 22
2*length + 2* width = 240

There are 6 fence posts for the length so 5 15-foot intervals between them, 75 feet
75*2 + 2* width = 240 then width = 45

If we double width = 90 then there are 6 15-foot intervals, as the result 7 fence posts for the width

7 + 7 + 6 + 6 - 4 = 22 ( we subtract 4 in order to avoid duplicates as 4 fences are vertices of the rectangular pasture)

Hope that helps

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Re: A rectangular pasture has fence posts along every side at 15-foot [#permalink]

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New post 11 Aug 2017, 00:10
Consider the rectangular pasture which has a perimeter of 240
2(Length + Breadth) = 240 => Length + Breadth = 120

It has been given that the fence posts along each side are available at 15 foot intervals.
Since, there are 6 fence posts, along the length, length can be 75 with posts at both ends of the length.
This makes the Breadth of the pasture 45.
Since the new pasture has double the width, the new width is 90.
We will have 6 fence posts across the length and 5 posts across the new width of the pasture.

Hence, we will have 22 posts across this new pasture(where the width is double that of the older pasture)(Option D)
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Re: A rectangular pasture has fence posts along every side at 15-foot [#permalink]

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New post 11 Aug 2017, 00:12
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azelastine wrote:
A rectangular pasture has fence posts along every side at 15-foot intervals. If there are 6 fence posts along the length of the pasture and the perimeter of the pasture is 240 feet, how many fence posts would surround this pasture if the width were doubled? (Assume that the space taken up by the fence posts is negligible.)

A) 14
B) 16
C) 20
D) 22
E) 24


Think of it this way:

6 fence posts along the length means 1 at the beg and 1 at the end with 4 in the middle and in all, five 15-foot gaps, a total of 75 feet in them. The other length will be the same 6 posts with 75 feet between them.

P_________P__________P__________P___________P__________P



P_________P__________P__________P___________P__________P

Since the perimeter of the pasture is 240 feet, and combined length is 150 feet, the combined width is 90 feet which means each width is 45 feet. Hence, in all we will have 4 posts on the width including the ends.


P_________P__________P__________P___________P__________P
:
;
P
:
:
P
:
:
P_________P__________P__________P___________P__________P

If we double the width, we get 90 feet width which needs 7 posts (including the ends)

P_________P__________P__________P___________P__________P
:
;
P
:
:
P
:
:
P
:
;
P
:
:
P
:
:
P_________P__________P__________P___________P__________P

In all, we have 6 + 6 + 5 + 5 = 22 posts
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Re: A rectangular pasture has fence posts along every side at 15-foot   [#permalink] 11 Aug 2017, 00:12
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