3 girls go to the beach , B walks, M rides her bike, and T takes a bus. It’s 6 miles to the beach B can be represented by y = 4x

M can be represented by y =8x - 4
And T can be represented by y = 20x -20
B leaves directly after school and M leads half an hour after B and T leaves an hour after B Which girl arrives first
B starts at O hours ending at 6 miles
M starts at 0.5 hours
T starts at 1 hour

1 answer

To determine which girl arrives first at the beach, we can analyze each girl's distance function and their respective departure times.

Equations Analysis:

  1. B's Equation: \( y = 4x \)

    • This means that B travels at a speed of 4 miles per hour.
  2. M's Equation: \( y = 8x - 4 \)

    • This indicates that M travels at a speed of 8 miles per hour.
  3. T's Equation: \( y = 20x - 20 \)

    • T travels at a speed of 20 miles per hour.

Departure Times:

  • B leaves at \( t = 0 \) hours.
  • M leaves at \( t = 0.5 \) hours.
  • T leaves at \( t = 1 \) hour.

Arrival Times Calculation:

  1. B's Arrival Time:

    • Distance to beach is 6 miles.
    • Using \( y = 4x \) for B, we set \( y = 6 \): \[ 6 = 4x \Rightarrow x = \frac{6}{4} = 1.5 \text{ hours} \]
    • Therefore, B arrives at \( 0 + 1.5 = 1.5 \) hours.
  2. M's Arrival Time:

    • M leaves at \( t = 0.5 \).
    • For M, using \( y = 8x - 4 \): \[ 6 = 8x - 4 \Rightarrow 8x = 10 \Rightarrow x = \frac{10}{8} = 1.25 \text{ hours} \]
    • Total time from the start of B's journey: \[ 0.5 + 1.25 = 1.75 \text{ hours} \]
    • Therefore, M arrives at \( 1.75 \) hours.
  3. T's Arrival Time:

    • T leaves at \( t = 1 \).
    • For T, using \( y = 20x - 20 \): \[ 6 = 20x - 20 \Rightarrow 20x = 26 \Rightarrow x = \frac{26}{20} = 1.3 \text{ hours} \]
    • Total time from the start of B's journey: \[ 1 + 1.3 = 2.3 \text{ hours} \]
    • Therefore, T arrives at \( 2.3 \) hours.

Conclusion:

  • B's arrival time: 1.5 hours
  • M's arrival time: 1.75 hours
  • T's arrival time: 2.3 hours

Thus, B arrives first at 1.5 hours.