Tim is a bus driver. He drives \( 101 / 2 \) miles in the morning and \( 109 / 10 \) miles in the afternoon. How many miles does he drive in all? Write your answer as a fraction or as a whole or mixed number. miles

To find out how many miles Tim drives in total, we first need to add the two distances he drives. In the morning, he drives \( \frac{101}{2} \) miles and in the afternoon, he drives \( \frac{109}{10} \) miles. To add these fractions, we need a common denominator. The least common multiple of 2 and 10 is 10. Now, we convert \( \frac{101}{2} \) to a fraction with a denominator of 10: \[ \frac{101}{2} = \frac{101 \times 5}{2 \times 5} = \frac{505}{10} \] Now that we have both fractions with the same denominator, we can add them: \[ \frac{505}{10} + \frac{109}{10} = \frac{505 + 109}{10} = \frac{614}{10} \] Next, we simplify \( \frac{614}{10} \) by dividing both the numerator and denominator by 2: \[ \frac{614 \div 2}{10 \div 2} = \frac{307}{5} \] Finally, we convert \( \frac{307}{5} \) into a mixed number: \[ 307 \div 5 = 61 \text{ remainder } 2 \] So, \( \frac{307}{5} = 61 \frac{2}{5} \). Thus, Tim drives a total of \( 61 \frac{2}{5} \) miles.