To find the total time spent driving, we need to add the three time durations together:
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Convert all the times into improper fractions:
- \( \frac{5}{6} \) hours is already an improper fraction.
- \( 2 \frac{1}{8} \) hours can be converted as follows: \[ 2 \frac{1}{8} = \frac{16}{8} + \frac{1}{8} = \frac{17}{8} \]
- \( 3 \frac{1}{2} \) hours can be converted as follows: \[ 3 \frac{1}{2} = \frac{6}{2} + \frac{1}{2} = \frac{7}{2} \]
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Find a common denominator:
The denominators are 6, 8, and 2. The least common multiple of these numbers is 24.- Convert \( \frac{5}{6} \) to a denominator of 24: \[ \frac{5}{6} = \frac{5 \times 4}{6 \times 4} = \frac{20}{24} \]
- Convert \( \frac{17}{8} \) to a denominator of 24: \[ \frac{17}{8} = \frac{17 \times 3}{8 \times 3} = \frac{51}{24} \]
- Convert \( \frac{7}{2} \) to a denominator of 24: \[ \frac{7}{2} = \frac{7 \times 12}{2 \times 12} = \frac{84}{24} \]
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Add the fractions together: \[ \frac{20}{24} + \frac{51}{24} + \frac{84}{24} = \frac{20 + 51 + 84}{24} = \frac{155}{24} \]
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Convert \( \frac{155}{24} \) to a mixed number:
- Divide 155 by 24: \[ 155 \div 24 = 6 \quad \text{(with a remainder of } 11\text{)} \]
- Therefore, \( \frac{155}{24} = 6 \frac{11}{24} \).
Thus, the total time spent driving by you and your friends is:
6 \(\frac{11}{24}\) hours.
Correct response: 6 11/24 hours.