Final answer:
To calculate the total number of hours Dan was driving, divide the total gallons of gas used by the gallons of gas used per hour. Upon calculation, it's found that he drove for approximately 10.83 hours, which would be rounded to 11 hours when considering whole number options.
Step-by-step explanation:
The student has asked how many hours Dan was driving if he used a total of 3 1/4 gallons of gas and each hour he used 3/10 gallons of gas. To find the total number of hours, one would divide the total gallons of gas used by the gallons of gas used per hour.
Converting 3 1/4 gallons to an improper fraction gives us 13/4 gallons. Dividing this by 3/10 gallons/hour will give us the total hours:
\(\frac{13/4}{3/10} = \frac{13}{4} \times \frac{10}{3} = \frac{130}{12} = 10.83\) hours.
However, since the options provided are all whole numbers, we realize that the calculation was intended to be:
\(\frac{(3\times4 + 1)}{4} \div \frac{3}{10} = \frac{13}{4} \div \frac{3}{10} = \frac{13}{4} \times \frac{10}{3} = \frac{13 \times 10}{4 \times 3} = \frac{130}{12}\)
Which simplifies further to:
\(\frac{130}{12} = 10.83\) hours. But since the options provide whole numbers, the closest answer would be 11 hours.