Difference between revisions of "1997 AIME Problems/Problem 7"
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\end{eqnarray*}</cmath> | \end{eqnarray*}</cmath> | ||
− | Noting that <math>\frac 12(t_1+t_2)</math> is at the maximum point of the parabola, we can use <math>\frac{ | + | Noting that <math>\frac 12(t_1+t_2)</math> is at the maximum point of the parabola, we can use <math>-\frac{b}{2a} = \frac{110}{2 \cdot \frac{5}{18}} = \boxed{198}</math>. |
== See also == | == See also == |
Revision as of 02:46, 29 June 2011
Problem
A car travels due east at mile per minute on a long, straight road. At the same time, a circular storm, whose radius is miles, moves southeast at mile per minute. At time , the center of the storm is miles due north of the car. At time minutes, the car enters the storm circle, and at time minutes, the car leaves the storm circle. Find .
Solution
We set up a coordinate system, with the starting point of the car at the origin. At time , the car is at and the center of the storm is at . Using the distance formula,
Noting that is at the maximum point of the parabola, we can use .
See also
1997 AIME (Problems • Answer Key • Resources) | ||
Preceded by Problem 6 |
Followed by Problem 8 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |