MathDB

Two skaters, Allie and Billie, are at points

A

and

B

, respectively, on a flat, frozen lake. The distance between

A

and

B

100

meters. Allie leaves

A

and skates at a speed of

8

meters per second on a straight line that makes a

60^\circ

angle with

AB

. At the same time Allie leaves

A

, Billie leaves

B

at a speed of

7

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?
[asy] defaultpen(linewidth(0.8)); draw((100,0)--origin--60*dir(60), EndArrow(5)); label("

A

", origin, SW); label("

B

", (100,0), SE); label("

100

", (50,0), S); label("

60^\circ

", (15,0), N);[/asy]

Problem Statement