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>C</math>. | + | ==Problem== |
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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 | ||
| + | \textbf{(B)}\ 16 \qquad | ||
| + | \textbf{(C)}\ 17 \qquad | ||
| + | \textbf{(D)}\ 18 \qquad | ||
| + | \textbf{(E)}\ \sqrt{32}+\sqrt{137}</math> | ||
| + | |||
| + | ==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 <math>8, 15, 17</math> Pythagorean triple, so the answer is <math>17</math>, which is <math>\boxed{\textbf{(C)}}</math>. | ||
| + | |||
| + | ==See Also== | ||
| + | {{AHSME 30p box|year=1973|num-b=19|num-a=21}} | ||
| + | |||
| + | [[Category:Introductory Geometry Problems]] | ||
Latest revision as of 13:02, 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
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 
Pythagorean triple, so the answer is 
, which is 
.
See Also
| 1973 AHSME (Problems • Answer Key • Resources) | ||
| 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 | ||
