your question is completely twisted in wrong way
let me give you correct question and answer
suppose initially bucket is full with C tokens , in token bucket algorithm each data packet first takes a token from bucket and then it enters in network from output end of bucket .
so initially for C packets we will have C tokens(since bucket is full) and remaining packets will take P*t tokens in time of t units where P is rate at which token enters in bucket
so the number of packets comes out of bucket in time t will be ( C+ P*t)
therefore maximum burst rate will be M = (C+P*t)/t
after simplification , we have t= C/(M-P) which is S in your question
hence it is minimum time which is = C/(M-P) not the maximum transmission rate .