Salena, Justin, and Brandon were riding their bikes to the library after school. The library is

12
1
2
miles from school. Salena rides her bike
2
1
2
miles every
5
minutes. Justin rides his bike
5
3
4
miles every
12
minutes. Brandon rides his bike
1
1
4
miles every
2
5
8
minutes.

If they all leave school at the same exact time and follow the same exact path to the library, which person will arrive at the library first?

Responses

Brandon
Brandon

There is no way to determine who will arrive first.
There is no way to determine who will arrive first.

Justin
Justin

Salena

1 answer

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).

  1. Calculate the speed of each biker:

    • 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 = \( \frac{2.5 \text{ miles}}{5 \text{ minutes}} = 0.5 \text{ miles/minute} \).
    • 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 = \( \frac{5.75 \text{ miles}}{12 \text{ minutes}} \approx 0.479 \text{ miles/minute} \).
    • 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 = \( \frac{1.25 \text{ miles}}{25.8 \text{ minutes}} \approx 0.0488 \text{ miles/minute} \).
  2. Calculate the time it takes for each person to reach the library:

    • Salena:

      • Time = \( \frac{\text{distance}}{\text{speed}} = \frac{12.5 \text{ miles}}{0.5 \text{ miles/minute}} = 25 \text{ minutes} \).
    • Justin:

      • Time = \( \frac{12.5 \text{ miles}}{0.479 \text{ miles/minute}} \approx 26.09 \text{ minutes} \).
    • Brandon:

      • Time = \( \frac{12.5 \text{ miles}}{0.0488 \text{ miles/minute}} \approx 256.61 \text{ minutes} \).
  3. 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