$(Q\to R)\wedge (R\to Q)$ converting to sentence
Your answer and the professor's answer are both correct.  Other ways to say $p$ implies $q$ are: "if $p$ then $q$" and "$p$ only if $q$".  You can replace "only if" by "implies".  

Thus, "I have time ONLY IF I will go to town" and "IF I have time I will go to town" both say the same thing - "I have time implies I will go to town".