1973 AHSME Problems/Problem 20

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 $\boxed{\textbf{(C)}}$ .

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

Page

Toolbox

Search

1973 AHSME Problems/Problem 20

Problem

Solution

See Also