Difference between revisions of "1989 AIME Problems/Problem 6"
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== Problem == | == Problem == | ||
| + | Two skaters, Allie and Billie, are at points <math>A^{}_{}</math> and <math>B^{}_{}</math>, respectively, on a flat, frozen lake. The distance between <math>A^{}_{}</math> and <math>B^{}_{}</math> is <math>100^{}_{}</math> meters. Allie leaves <math>A^{}_{}</math> and skates at a speed of <math>8^{}_{}</math> meters per second on a straight line that makes a <math>60^\circ</math> angle with <math>AB^{}_{}</math>. At the same time Allie leaves <math>A^{}_{}</math>, Billie leaves <math>B^{}_{}</math> at a speed of <math>7^{}_{}</math> 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? | ||
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| + | [[Image:AIME_1989_Problem_6.png]] | ||
== Solution == | == Solution == | ||
| + | {{solution}} | ||
== See also == | == See also == | ||
| + | * [[1989 AIME Problems/Problem 7|Next Problem]] | ||
| + | * [[1989 AIME Problems/Problem 5|Previous Problem]] | ||
* [[1989 AIME Problems]] | * [[1989 AIME Problems]] | ||
Revision as of 22:02, 24 February 2007
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
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