Question

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

Answer 1

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**.