We call the point where A & B start: Zero point ( 0 point), the point "x" meters away from "0" point in the direction that A & B move : the point x.
Speed discrepancy between A & B : 400 - 250 = 150
If A & B meet, A must move faster than B a distance that is the multiple of 100m ( a fulll circle)
the first time they meet is after : 100/150 = 2/3 hour, the position of the point: 2/3 * 250 = 166.66 m or at point 66.6
the second time they meet is after another 2/3 hour , the position of the point: (2/3) * 2 * 250 = 333.3 or at point 33.3
the third time they meet is 2/3 hour after their second meet, the position of the point: (2/3) * 3 * 250 = 500 or at point "0"
Now we get the rule: the forth point will be at point 66.6, the fifth: point 33.3, the sixth: point zero, and so on.
So there're only three positions that A & B will meet
This is the rule that I figure out ( IMO only, not from any official sources) :
Circle length : 100
Speed discrepancy : 150
time between each meets: 100/150 = 2/3 ( note that you must simplify the fraction as much as possible, for instance 6/15 must be changed to 2/5)
the number of points is the smallest positive integer that multiplies to "2/3" will give out an integer. This case is 3
Take another example:
A's speed : 500
B's speed: 200
Circle's length: 400
Speed Discrepancy: 300
Time period: 400/300 = 4/3
No. of points A & B will meet : 3 ( as 3 is the smallest positive integer that multiplies to 4/3 to give out an integer)
Last edited by
limestone on Mon Sep 13, 2010 12:31 pm, edited 1 time in total.
