To find the total driving time, we will first convert all the time each person drove into fractions and then add them together.
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Convert the times into improper fractions:
- \( \frac{5}{6} \) hour is already a fraction.
- \( 2 \frac{1}{8} \) hours can be converted: \( 2 \times 8 + 1 = 16 + 1 = 17 \), thus it becomes \( \frac{17}{8} \).
- \( 3 \frac{1}{2} \) hours can be converted: \( 3 \times 2 + 1 = 6 + 1 = 7 \), thus it becomes \( \frac{7}{2} \).
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Now, we can express all fractions with a common denominator. The denominators we have are 6, 8, and 2. The least common multiple of these numbers is 24.
- Convert \( \frac{5}{6} \) to have a denominator of 24: \[ \frac{5}{6} = \frac{5 \times 4}{6 \times 4} = \frac{20}{24} \]
- Convert \( \frac{17}{8} \) to have a denominator of 24: \[ \frac{17}{8} = \frac{17 \times 3}{8 \times 3} = \frac{51}{24} \]
- Convert \( \frac{7}{2} \) to have a denominator of 24: \[ \frac{7}{2} = \frac{7 \times 12}{2 \times 12} = \frac{84}{24} \]
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Now, we add the fractions: \[ \frac{20}{24} + \frac{51}{24} + \frac{84}{24} = \frac{20 + 51 + 84}{24} = \frac{155}{24} \]
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Convert \( \frac{155}{24} \) into a mixed number:
- Divide 155 by 24: \[ 155 \div 24 = 6 \quad \text{(remainder: } 11\text{)} \]
- So, \( \frac{155}{24} = 6 \frac{11}{24} \) hours.
Thus, the total time spent driving by all three friends is:
6 11/24 hours.
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