Difference between revisions of "1961 AHSME Problems/Problem 2"
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Rockmanex3 (talk | contribs) (Solution to Problem 2) |
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| − | An automobile travels a/6 | + | == Problem == |
| + | |||
| + | An automobile travels <math>a/6</math> feet in <math>r</math> seconds. If this rate is maintained for <math>3</math> minutes, how many yards does it travel in <math>3</math> minutes? | ||
| + | |||
| + | <math>\textbf{(A)}\ \frac{a}{1080r}\qquad | ||
| + | \textbf{(B)}\ \frac{30r}{a}\qquad | ||
| + | \textbf{(C)}\ \frac{30a}{r}\qquad | ||
| + | \textbf{(D)}\ \frac{10r}{a}\qquad | ||
| + | \textbf{(E)}\ \frac{10a}{r} </math> | ||
| + | |||
| + | ==Solution== | ||
| + | Use dimensional analysis. | ||
| + | <cmath>\frac{a/6 \text{ feet}}{r \text{ seconds}} \cdot \frac{1 \text{ yard}}{3 \text{ feet}} \cdot \frac{60 \text{ seconds}}{1 \text{ minute}} \cdot 3 \text{ minutes}</cmath> | ||
| + | <cmath>\frac{10a}{r} \text{ yards}</cmath> | ||
| + | The answer is <math>\boxed{\textbf{(E)}}</math>. | ||
| + | |||
| + | ==See Also== | ||
| + | {{AHSME 40p box|year=1961|num-b=1|num-a=3}} | ||
| + | |||
| + | {{MAA Notice}} | ||
Latest revision as of 19:30, 17 May 2018
Problem
An automobile travels 
feet in 
seconds. If this rate is maintained for 
minutes, how many yards does it travel in minutes?
Solution
Use dimensional analysis.
![\[\frac{a/6 \text{ feet}}{r \text{ seconds}} \cdot \frac{1 \text{ yard}}{3 \text{ feet}} \cdot \frac{60 \text{ seconds}}{1 \text{ minute}} \cdot 3 \text{ minutes}\]](http://latex.artofproblemsolving.com/1/0/a/10af9c1e845ef83f1f53e816f9dbdfd693e8ea8f.png)
![\[\frac{10a}{r} \text{ yards}\]](http://latex.artofproblemsolving.com/3/8/8/3889d8f019bb3f94371d0bc70e0a5251cb6d90e5.png)
The answer is 
.
See Also
| 1961 AHSC (Problems • Answer Key • Resources) | ||
| Preceded by Problem 1 |
Followed by Problem 3 | |
| 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 • 36 • 37 • 38 • 39 • 40 | ||
| All AHSME Problems and Solutions | ||
These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. 
