James and Henry are at the northwest corner of their busines

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James and Henry are at the northwest corner of their busines [#permalink]

13 Nov 2012, 04:22

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James and Henry are at the northwest corner of their business school’s football field, which is a rectangle 300 ft long and 160 ft wide. James walks in a straight line directly to the southeast corner of the field. If Henry walks 180 ft down the west side of the field and then walks in a straight line directly to the southeast corner of the field, how many feet farther, to the nearest 10 ft, will Henry walk than James?

A. 20
B. 40
C. 80
D. 120
E. 140

[Reveal] Spoiler: OA

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Re: James and Henry are at the northwest corner of their busines [#permalink]

13 Nov 2012, 04:52

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gmatbull wrote:

Look at the diagram below:

Attachment:

Football field.png [ 5.69 KiB | Viewed 642 times ]

The distance covered by James (AD) is shown in blue and it equals to \sqrt{300^2+160^2}=\sqrt{10^2(30^2+16^2)}=10*\sqrt{1156}=340;

The distance covered by Henry (AB+BD) is shown in red and it equals to 180+\sqrt{120^2+160^2}=180+\sqrt{10^2(12^2+16)^2}=180+10\sqrt{400}=380;

The difference is 380-340=40.

Answer: B.
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Director

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Re: James and Henry are at the northwest corner of their busines [#permalink]

14 Nov 2012, 00:52

Thanks Bunuel for your lucid explanations as usual.
I misinterpreted the text below:
"If Henry walks 180 ft down the west side of the field " to mean
"Henry walks 180 ft westwards"; Sure, that was a misleading interpretation.

Actually, Henry walked DOWNWARD, but on the western wing of the field.
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Re: James and Henry are at the northwest corner of their busines [#permalink]

17 Nov 2012, 13:04

How do we decide the rectangle layout to be? I took 300 to be the length from northeast to east whereas in the explanation it takes 160 for the same length.

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Re: James and Henry are at the northwest corner of their busines [#permalink]

18 Nov 2012, 00:22

rashmilagisetty wrote:

How do we decide the rectangle layout to be? I took 300 to be the length from
northeast to east whereas in the explanation it takes 160 for the same length.

Which ever orientation u prefer doesn't change the fact that it remains a rectangle as shown in the attached.
However, note that If Henry walks 180 ft down the west side of the field, the
vertical side must be the side with 300 ft.

Attachments

james n Henry.jpg [ 8.93 KiB | Viewed 457 times ]

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Re: James and Henry are at the northwest corner of their busines [#permalink] 18 Nov 2012, 00:22

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James and Henry are at the northwest corner of their busines

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James and Henry are at the northwest corner of their busines

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