Kinematics of motion in a straight line — practice question

The velocity-time graphs in the diagram describe the motion of two particles $P$ and $Q$, both moving in the same direction along a straight line. $P$ and $Q$ begin from the same point $X$ on the line, although $Q$ begins $T\,\text{s}$ after $P$. For the first $20\,\text{s}$ of motion, each particle travels at speed $2.5\,\text{m s}^{-1}$. Once each has been moving for $20\,\text{s}$, its speed increases instantaneously to $4\,\text{m s}^{-1}$ and then stays at that speed. It is given that $P$ has covered $70\,\text{m}$ at the moment $Q$ begins.