To find the difference in time between Elisha and Lewis, we first need to convert their times into improper fractions.
Elisha's time is \( 7 \frac{1}{6} \) minutes: \[ 7 \frac{1}{6} = \frac{7 \times 6 + 1}{6} = \frac{42 + 1}{6} = \frac{43}{6} \text{ minutes} \]
Lewis's time is \( 8 \frac{3}{4} \) minutes: \[ 8 \frac{3}{4} = \frac{8 \times 4 + 3}{4} = \frac{32 + 3}{4} = \frac{35}{4} \text{ minutes} \]
Now, we need to find a common denominator to subtract these fractions. The least common multiple of 6 and 4 is 12.
Next, we convert both fractions:
Elisha's time in terms of twelfths: \[ \frac{43}{6} = \frac{43 \times 2}{6 \times 2} = \frac{86}{12} \text{ minutes} \]
Lewis's time in terms of twelfths: \[ \frac{35}{4} = \frac{35 \times 3}{4 \times 3} = \frac{105}{12} \text{ minutes} \]
Now, we can subtract Elisha's time from Lewis's time to find the difference: \[ \frac{105}{12} - \frac{86}{12} = \frac{105 - 86}{12} = \frac{19}{12} \text{ minutes} \]
To express \( \frac{19}{12} \) as a mixed number: \[ \frac{19}{12} = 1 \frac{7}{12} \text{ minutes} \]
Thus, the time that separates the two runners is \( 1 \frac{7}{12} \) minutes.
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