Two hikers begin at the same initial location and walk around a circular lake in opposite directions.One walks twice as fast as the other.The circumference of the lake is L.How far does the faster hiker walk before the two hikers meet at the same final location?
A)L/3
B)L/2
C)2L/3
D)3L/4

Question

Quizplus · Accepted Answer

Let the slower hiker's speed be x and faster hiker's speed be 2x. Let the distance walked by slower hiker be d. Then distance walked by faster hiker is 2d.
When both hikers meet, the slower hiker would have walked (d/L)*360 degrees and the faster hiker would have walked (2d/L)*360 degrees. Since they meet at the same location, the sum of their degree traversed should be 360 degrees. This gives:

(d/L)*360 + (2d/L)*360 = 360
d/L + 2d/L = 1
d = L/3

So, the distance walked by the faster hiker before they meet is 2d = 2 * (L/3) = 2L/3. Therefore, the answer is C.

Two Hikers Begin at the Same Initial Location and Walk