# Question #51957

Feb 26, 2017

They will never meet each other.

#### Explanation:

The question should state:
Three boys A, B, and C are situated at the $v e r t i c e s$,
otherwise the three boys would already be together at one vertex.

One of the boys moves towards one other with constant speed $v$.
The speed $v$ of each boy is identical to that of the other two.
The distance $d$ travelled by each boy is identical for all.
Then as time increases, the distance travelled by each boy remains the same.

In this question we are given: A always moves towards B, B towards C, and C towards A, resulting in the vectors:

$A \to B , B \to C , C \to A$

Since the motion of each boy is continuously identical in a direction around the perimeter of the triangle, they will never meet.

Note: This question is $s i m i l a r$ to the complex one on quora: https://www.quora.com/There-are-3-points-placed-on-the-vertices-of-an-equilateral-triangle-of-side-A-Each-point-travels-with-a-constant-speed-of-v-directly-to-the-next-point-How-much-time-does-it-take-for-the-three-points-to-meet