Jacopo,
We have not discussed enough in this course for you to tackle such a scenario (with circuit switches and different transmission rates).
Consider a link L1, a circuit switch, then a link L2.
The way we described things in class, when the circuit switch connects L1 and L2 (closes the corresponding physical circuit), then L1 and L2 essentially become one link, so they cannot have "different transmission rates" any more. They are one link with one transmission rate. How to determine the value of this transmission rate? That depends on the materials that are involved (the physical layer). E.g., if L1 and L2 are made of copper cables, and we use a connector to connect them together, the transmission rate of the resulting link depends on the properties of the two cables and the connector -- we would need mathematical models of the corresponding communication channels and what happens when we put them in sequence.
Very interesting but clearly outside the scope of COM-208.