Difference between revisions of "2014 AMC 8 Problems/Problem 25"
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| − | + | A straight one-mile stretch of highway, <math>40</math> feet wide, is closed. Robert rides his bike on a path composed of semicircles as shown. If he rides at <math>5</math> miles per hour, how many hours will it take to cover the one-mile stretch? | |
| − | + | ||
| + | Note: <math>1</math> mile= <math>5280</math> feet | ||
| + | |||
| + | <asy> | ||
| + | size(10cm); pathpen=black; pointpen=black; | ||
| + | D(arc((-2,0),1,300,360)); | ||
| + | D(arc((0,0),1,0,180)); | ||
| + | D(arc((2,0),1,180,360)); | ||
| + | D(arc((4,0),1,0,180)); | ||
| + | D(arc((6,0),1,180,240)); | ||
| + | D((-1.5,1)--(5.5,1)); | ||
| + | D((-1.5,0)--(5.5,0),dashed); | ||
| + | D((-1.5,-1)--(5.5,-1)); | ||
| + | </asy> | ||
| + | |||
| + | <math> \textbf{(A) }\frac{\pi}{11}\qquad\textbf{(B) }\frac{\pi}{10}\qquad\textbf{(C) }\frac{\pi}{5}\qquad\textbf{(D) }\frac{2\pi}{5}\qquad\textbf{(E) }\frac{2\pi}{3} </math> | ||
==See Also== | ==See Also== | ||
{{AMC8 box|year=2014|num-b=24|num-a=Last Problem}} | {{AMC8 box|year=2014|num-b=24|num-a=Last Problem}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Revision as of 19:31, 26 November 2014
A straight one-mile stretch of highway, 
feet wide, is closed. Robert rides his bike on a path composed of semicircles as shown. If he rides at 
miles per hour, how many hours will it take to cover the one-mile stretch?
Note: 
mile= 
feet
![[asy] size(10cm); pathpen=black; pointpen=black; D(arc((-2,0),1,300,360)); D(arc((0,0),1,0,180)); D(arc((2,0),1,180,360)); D(arc((4,0),1,0,180)); D(arc((6,0),1,180,240)); D((-1.5,1)--(5.5,1)); D((-1.5,0)--(5.5,0),dashed); D((-1.5,-1)--(5.5,-1)); [/asy]](http://latex.artofproblemsolving.com/0/4/9/049ce19ef0018e1432783b07f794e12741919e00.png)
See Also
| 2014 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 24 |
Followed by Problem Last Problem | |
| 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 | ||
| All AJHSME/AMC 8 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
