\begin{tabular}{|c|c|c|c|c|}
\hline $\begin{array}{c}\text { Time } \\
\text { (hours) }\end{array}$ & $\frac{1}{2}$ & 1 & $1 \frac{1}{2}$ & 2 \\
\hline $\begin{array}{c}\text { Charge } \\
\text { (\$) }\end{array}$ & & & & 110 \\
\hline
\end{tabular}

Step 1 ：Given that the charge for 2 hours is $110, we can assume that the charge is proportional to the time.

Step 2 ：Calculate the charge per hour by dividing the total charge by the total time. \(\frac{110}{2} = 55\)

Step 3 ：Use the charge per hour to find the charges for the other times. For half an hour, the charge is \(\frac{1}{2} \times 55 = 27.5\). For 1 hour, the charge is \(1 \times 55 = 55\). For 1 and a half hours, the charge is \(\frac{3}{2} \times 55 = 82.5\)

Step 4 ：\(\boxed{\text{The charges for }\frac{1}{2}\text{ hour, 1 hour, and }1 \frac{1}{2}\text{ hours are }\$27.5, \$55.0, \text{ and }\$82.5\text{ respectively.}}\)