examday

/TMUA

Three points $P,Q,R$ start at the vertices $A,B,C$, respectively, of a triangle. They travel along $AB,BC,CA$, respectively, at constant speeds, reaching the other endpoint after $1$, $2$ and $3$ seconds, respectively. Each point stops when it reaches that endpoint.

For how long during the first $3$ seconds is the area of triangle $PQR$ at most one third of the area of triangle $ABC$?

One possible position during the motion is shown.