Spanning-Tree Backbone Fast

i think i get it now, i reread it. so without backbonefast, Switch C will drop the inferior BPDU produced by Switch B. since the link A-B is down, Switch C f0/16 is not receiving the old BPDU so it will wait for the max age time to expire (20secs), then it will now go to listening and learning state.

when backbonefast is enabled, switch C will not drop/ignore the inferior BPDU, C will send a RLQ to the root bridge, then if C receives a response, it means root bridge is alive, then it will skip the max age time on F0/16 then will go to listening and learning, then in forwarding state, C will inform B that Root bridge is alive.