To determine who will arrive at the library first, we need to calculate the speeds of Salena, Justin, and Brandon and then figure out how long it takes each of them to reach the library, which is \( 12 \frac{1}{2} \) miles (or \( 12.5 \) miles).
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Calculate the speed of each biker:
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Salena:
- She rides \( 2 \frac{1}{2} \) miles every \( 5 \) minutes.
- Convert \( 2 \frac{1}{2} \) to a decimal: \( 2 \frac{1}{2} = 2.5 \) miles.
- Speed = \( \frac{2.5 \text{ miles}}{5 \text{ minutes}} = 0.5 \text{ miles/minute} \).
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Justin:
- He rides \( 5 \frac{3}{4} \) miles every \( 12 \) minutes.
- Convert \( 5 \frac{3}{4} \) to a decimal: \( 5 \frac{3}{4} = 5.75 \) miles.
- Speed = \( \frac{5.75 \text{ miles}}{12 \text{ minutes}} \approx 0.479 \text{ miles/minute} \).
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Brandon:
- He rides \( 1 \frac{1}{4} \) miles every \( 25 \frac{8}{10} \) minutes (or \( 25.8 \) minutes).
- Convert \( 1 \frac{1}{4} \) to a decimal: \( 1 \frac{1}{4} = 1.25 \) miles.
- Speed = \( \frac{1.25 \text{ miles}}{25.8 \text{ minutes}} \approx 0.0488 \text{ miles/minute} \).
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Calculate the time it takes for each person to reach the library:
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Salena:
- Time = \( \frac{\text{distance}}{\text{speed}} = \frac{12.5 \text{ miles}}{0.5 \text{ miles/minute}} = 25 \text{ minutes} \).
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Justin:
- Time = \( \frac{12.5 \text{ miles}}{0.479 \text{ miles/minute}} \approx 26.09 \text{ minutes} \).
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Brandon:
- Time = \( \frac{12.5 \text{ miles}}{0.0488 \text{ miles/minute}} \approx 256.61 \text{ minutes} \).
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Conclusion:
- Salena: \( 25 \) minutes
- Justin: \( \approx 26.09 \) minutes
- Brandon: \( \approx 256.61 \) minutes
Thus, Salena will arrive at the library first. Therefore, the correct response is:
Salena