Question

Three people standing at the corners of an equilateral triangle start from rest and move with the same speed v along the triangle . The side of the triangle is a. After what time will they meet?

Answer 1

If the people are always moving along the original triangle, they will never meet. However if they are always pointing towards the next, then they will meet.

Velocity of approach
$=V+Vcos{60}^{\circ }$
$=\frac{3V}{2}$
$\therefore$ Time $=\frac{separation}{velocityofapproach}$
$=\frac{d}{\frac{3V}{2}}=\frac{2d}{3v}$