AMC 10 2022a

What is the value of $$3 + \frac{1}{3+\frac{1}{3+\frac{1}{3}}}?$$ $\textbf{(A) } \frac{31}{10} \textbf{(B) } \frac{49}{15} \textbf{(C) } \frac{33}{10} \textbf{(D) } \frac{109}{33} \textbf{(E) } \frac{15}{4}$

Mike cycled $15$ laps in $57$ minutes. Assume he cycled at a constant speed throughout. Approximately how many laps did he complete in the first $27$ minutes? $\textbf{(A) } 5 \textbf{(B) } 7 \textbf{(C) } 9 \textbf{(D) } 11 \textbf{(E) } 13$