To find the total time spent driving by you and your two friends, we need to add up the individual driving times.
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Convert the given times to a consistent format (hours):
- You drove: \( 56 \) minutes = \( \frac{56}{60} \) hours = \( \frac{14}{15} \) hours.
- Friend 1 drove: \( 2 \frac{1}{8} \) hours = \( 2 + \frac{1}{8} = \frac{16}{8} + \frac{1}{8} = \frac{17}{8} \) hours.
- Friend 2 drove: \( 3 \frac{1}{2} \) hours = \( 3 + \frac{1}{2} = \frac{6}{2} + \frac{1}{2} = \frac{7}{2} \) hours.
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Now, let's add these times together:
\[ \text{Total Time} = \frac{14}{15} + \frac{17}{8} + \frac{7}{2} \]
First, convert each term to a common denominator. The least common multiple of 15, 8, and 2 is 120.
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Convert \( \frac{14}{15} \): \[ \frac{14}{15} \times \frac{8}{8} = \frac{112}{120} \]
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Convert \( \frac{17}{8} \): \[ \frac{17}{8} \times \frac{15}{15} = \frac{255}{120} \]
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Convert \( \frac{7}{2} \): \[ \frac{7}{2} \times \frac{60}{60} = \frac{420}{120} \]
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Now add these fractions: \[ \frac{112}{120} + \frac{255}{120} + \frac{420}{120} = \frac{112 + 255 + 420}{120} = \frac{787}{120} \]
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Convert \(\frac{787}{120}\) into a mixed number:
- \( 787 ÷ 120 = 6\) remainder \(67\)
- Therefore, \( \frac{787}{120} = 6 \frac{67}{120}\).
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To express \(\frac{67}{120}\) as a fraction of an hour (for clarity in time): \[ 67 \text{ minutes} \text{ is approximately } 1 \text{ hour and } 7 \text{ minutes}. \]
So, the total driving time is \( 6 \frac{67}{120}\) hours or approximately \( 6.\) hours and \( 7 \text{minutes}.\)
Since that does not match the provided options exactly, the best approximate total from the options given would be:
6 1/4 hours.
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