To determine how long Mrs. Thomas will drive before stopping for gas, we need to find [tex]\( \frac{1}{3} \)[/tex] of her total trip time.
1. Convert the total trip time to a single fraction:
Mrs. Thomas's total trip time is given as [tex]\( 13 \frac{2}{3} \)[/tex] hours. To work with this more easily, we'll first convert this mixed number to an improper fraction.
[tex]\[
13 \frac{2}{3} = 13 + \frac{2}{3} = \frac{39}{3} + \frac{2}{3} = \frac{39 + 2}{3} = \frac{41}{3}
\][/tex]
2. Determine [tex]\( \frac{1}{3} \)[/tex] of the total trip time:
Since Mrs. Thomas wants to stop for gas after [tex]\( \frac{1}{3} \)[/tex] of the trip has passed, we'll calculate [tex]\( \frac{1}{3} \)[/tex] of [tex]\( \frac{41}{3} \)[/tex].
[tex]\[
\frac{1}{3} \times \frac{41}{3} = \frac{41}{9}
\][/tex]
3. Convert the result to decimal form:
To understand how long this is in hours, we convert [tex]\( \frac{41}{9} \)[/tex] to a decimal.
[tex]\[
\frac{41}{9} \approx 4.555555555555555
\][/tex]
Hence, Mrs. Thomas will drive approximately 4.56 hours before she stops for gas.
