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Mark and Kim are at the post office. To get home, Kim walks 3 miles no

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Math Expert
Joined: 02 Sep 2009
Posts: 58420
Mark and Kim are at the post office. To get home, Kim walks 3 miles no  [#permalink]

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25 Feb 2019, 02:28
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Difficulty:

45% (medium)

Question Stats:

62% (02:02) correct 38% (02:07) wrong based on 50 sessions

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Mark and Kim are at the post office. To get home, Kim walks 3 miles north and 2 miles west and Mark walks 8 miles south and 2 miles east. What is the approximate straight-line distance between Kim’s house and Mark’s house?

A. 10.1 miles
B. 11.7 miles
C. 12 miles
D. 13.2 miles
E. 15 miles

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Mark and Kim are at the post office. To get home, Kim walks 3 miles no  [#permalink]

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Updated on: 26 Feb 2019, 00:51
Bunuel wrote:
Mark and Kim are at the post office. To get home, Kim walks 3 miles north and 2 miles west and Mark walks 8 miles south and 2 miles east. What is the approximate straight-line distance between Kim’s house and Mark’s house?

A. 10.1 miles
B. 11.7 miles
C. 12 miles
D. 13.2 miles
E. 15 miles

plot values
we get
√(11^2 +4^2) = ~ 11.7 miles
IMO B

Originally posted by Archit3110 on 25 Feb 2019, 04:24.
Last edited by Archit3110 on 26 Feb 2019, 00:51, edited 2 times in total.
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Joined: 04 Jan 2015
Posts: 3078
Re: Mark and Kim are at the post office. To get home, Kim walks 3 miles no  [#permalink]

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25 Feb 2019, 23:57

Solution

Given:
• Mark and Kim are at the post office.
• To get home, Kim walks 3 miles north and 2 miles west and Mark walks 8 miles south and 2 miles east.

To find:
• The approximate straight-line distance between Kim’s house and Mark’s house

Approach and Working:

The figure represents the final position of Kim and Mark.
• Therefore, the approximate straight-line distance = $$\sqrt{4^2 + 11^2} = \sqrt{137}$$ = 11.7 miles

Hence, the correct answer is option B.

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Re: Mark and Kim are at the post office. To get home, Kim walks 3 miles no  [#permalink]

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01 Mar 2019, 11:01
Bunuel wrote:
Mark and Kim are at the post office. To get home, Kim walks 3 miles north and 2 miles west and Mark walks 8 miles south and 2 miles east. What is the approximate straight-line distance between Kim’s house and Mark’s house?

A. 10.1 miles
B. 11.7 miles
C. 12 miles
D. 13.2 miles
E. 15 miles

We can place the post office at the origin (0, 0) on the coordinate plane. Thus, Kim’s house would be at the point (-2, 3), and Mark’s house would be at the point (2, -8). Using the distance formula, we see that the distance between their houses is:

√[(-2 -2)^2 + (3 - (-8))^2] = √[(-4)^2 + 11^2] = √[16 + 121] = √137 ≈ 11.7

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Re: Mark and Kim are at the post office. To get home, Kim walks 3 miles no   [#permalink] 01 Mar 2019, 11:01
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