2018 AIME II Problems/Problem 1

Revision as of 23:13, 23 March 2018 by P groudon (talk | contribs) (Created page with "==Problem== Points <math>A</math>, <math>B</math>, and <math>C</math> lie in that order along a straight path where the distance from <math>A</math> to <math>C</math> is <mat...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

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 (ProblemsAnswer KeyResources)
Preceded by
First Problem
Followed by
Problem 2
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
All AIME Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. AMC logo.png