1989 AIME Problems/Problem 6
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Problem
Two skaters, Allie and Billie, are at points 
and 
, respectively, on a flat, frozen lake. The distance between and is 
meters. Allie leaves and skates at a speed of 
meters per second on a straight line that makes a 
angle with 
. At the same time Allie leaves , Billie leaves at a speed of 
meters per second and follows the straight path that produces the earliest possible meeting of the two skaters, given their speeds. How many meters does Allie skate before meeting Billie?
Solution
Label the point of intersection as 
. Since 
, 
and 
. According to the law of cosines,
Since we are looking for the earliest possible intersection, 
seconds are needed. Thus, 
meters is the solution.
See also
| 1989 AIME (Problems • Resources) | ||
| Preceded by Problem 5 | Followed by Problem 7 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
