2018 AIME II Problems/Problem 1

Problem

Points $A$ , $B$ , and $C$ lie in that order along a straight path where the distance from $A$ to $C$ is $1800$ meters. Ina runs twice as fast as Eve, and Paul runs twice as fast as Ina. The three runners start running at the same time with Ina starting at $A$ and running toward $C$ , Paul starting at $B$ and running toward $C$ , and Eve starting at $C$ and running toward $A$ . When Paul meets Eve, he turns around and runs toward $A$ . Paul and Ina both arrive at $B$ at the same time. Find the number of meters from $A$ to $B$ .

2018 AIME II (Problems • Answer Key • Resources)
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These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions.

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2018 AIME II Problems/Problem 1

Problem