Two moving points from the origin

Calculus Level 2

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

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