Three runners $A$, $B$ and $C$ run along parallel tracks with constant speed. On start the area of the triangle $ABC$ is equal to $2$. $5$ seconds later it is equal to $3$. What could it be $5$ more seconds later?
I understand that the area of a triangle is half the area of a parallelogram spanned by vectors corresponding to the position of the runners. So, we need to look at the sign of the determinant and its value. But I don’t understand how to solve the problem. I know that there are two possible answers: 8 and 4, but I don’t understand how to get them.
It is clear that the speed of the runners is different, and the area can either decrease from the start or increase. But what after?