Consider the following premises. If Barbara reads a book, then it is late. Charles is a cashier. If Charles were a cashier, then Barbara is reading a book. Can we infer the following from them? It is late.
 From the fact that if Charles were a cashier, then Barbara is reading a book, and that Charles is a cashier we can infer that Barbara is reading a book. Finally, from the fact that if Barbara reads a book, then it is late, and that Barbara is reading a book we can infer that it is late. Therefore, the answer is yes.