To find the total amount of time Sarah spends washing her mom's car, we first need to calculate how long she spends washing it, given that she spends four times as long washing as she does vacuuming.
Sarah spends \( \frac{1}{6} \) hour vacuuming.
So the time spent washing the car is: \[ 4 \times \frac{1}{6} = \frac{4}{6} = \frac{2}{3} \text{ hours} \]
Thus, the total amount of time Sarah spends washing her mom's car is \( \frac{2}{3} \) hour.