Answer: \(5\frac{1}{4}\ hours\)
Step-by-step explanation:
Given: Tanya drove car in \(\frac{1}{3}\) tank of gas= \(3\frac{1}{2}\) hours \(=\frac{7}{2}\) hours
Tanya drove car in a full tank of gas = \(\frac{\frac{7}{2}}{\frac{1}{3}}=\frac{7}{2}\times3=\frac{21}{2}\) hours
Tanya drove car in \(\frac{1}{2}\) tank of gas=\(\frac{21}{2}\times\frac{1}{2}=\frac{21}{4}=5\frac{1}{4}\ hours\)
Hence, Tanya drove \(5\frac{1}{4}\ hours\)car in \(\frac{1}{2}\) tank of gas.
