Difference between revisions of "1973 AHSME Problems/Problem 20"

 
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First, you draw a reflection of the cowboy across the river. Then, you draw the straight line from the "cowboy" to his cabin. This will be a <math>8, 15, 17</math> Pythagorean triple, so the answer is <math>17</math>, which is <math>\boxed{C}</math>.
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==Problem==
{{AHSME 35p box|year=1973|before=[[1972 AHSME]]|after=[[1974 AHSME]]}}
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A cowboy is 4 miles south of a stream which flows due east. He is also 8 miles west and 7 miles north of his cabin. He wishes to water his horse at the stream and return home. The shortest distance (in miles) he can travel and accomplish this is
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<math> \textbf{(A)}\ 4+\sqrt{185} \qquad
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\textbf{(B)}\ 16 \qquad
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\textbf{(C)}\ 17 \qquad
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\textbf{(D)}\ 18 \qquad
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\textbf{(E)}\ \sqrt{32}+\sqrt{137}</math>
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==Solution==
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First, you draw a reflection of the cowboy across the river. Then, you draw the straight line from the "cowboy" to his cabin. This will be a <math>8, 15, 17</math> Pythagorean triple, so the answer is <math>17</math>, which is <math>\boxed{\textbf{(C)}}</math>.
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==See Also==
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{{AHSME 30p box|year=1973|num-b=19|num-a=21}}
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[[Category:Introductory Geometry Problems]]

Latest revision as of 14:02, 20 February 2020

Problem

A cowboy is 4 miles south of a stream which flows due east. He is also 8 miles west and 7 miles north of his cabin. He wishes to water his horse at the stream and return home. The shortest distance (in miles) he can travel and accomplish this is

$\textbf{(A)}\ 4+\sqrt{185} \qquad \textbf{(B)}\ 16 \qquad \textbf{(C)}\ 17 \qquad \textbf{(D)}\ 18 \qquad \textbf{(E)}\ \sqrt{32}+\sqrt{137}$

Solution

First, you draw a reflection of the cowboy across the river. Then, you draw the straight line from the "cowboy" to his cabin. This will be a $8, 15, 17$ Pythagorean triple, so the answer is $17$, which is $\boxed{\textbf{(C)}}$.

See Also

1973 AHSME (ProblemsAnswer KeyResources)
Preceded by
Problem 19
Followed by
Problem 21
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35
All AHSME Problems and Solutions