Two moving points from the origin

Calculus Level 2

Two points $P$ and $Q$ start at the origin and move from the origin at the same time along the $x$ -axis. At time $t>0$ , $P$ and $Q$ have velocities of $\sin (\pi t)$ and $2\sin (2\pi t)$ , respectively. If $P$ and $Q$ first meet again after $\frac{m}{n}$ seconds, where $m$ and $n$ are positive co-prime integers, what is the value of $m+n$ ?