At time t0 the sending host begins

At time t0 the sending host begins to transmit. At time t1 = L/R1,
the sending host completes transmission and the entire packet is received at the router (no propagation delay).
Because the router has the entire packet at time t1, it can begin to transmit the packet to the receiving host at time t1.
At time t2 = t1 + L/R2, the router completes transmission and the entire packet is received at the receiving host (again, no propagation delay).
Thus, the end-to-end delay is L/R1 + L/R2.