Question

What are the equations and graph provided to determine which girl, Bethany, Morgan, or Taylor, arrives at the activity center first, and provide the time it takes for each girl to travel the 6 miles from the school to the activity center?

Answer 1

To determine which girl arrives at the activity center first, we need to know their respective speeds and the distance they are traveling. Since they all travel the same distance (6 miles), we can use the basic formula for time:

\[
\text{Time} = \frac{\text{Distance}}{\text{Speed}}
\]

If you have the speeds for Bethany, Morgan, and Taylor, you can calculate the time for each one to reach the activity center.

### Example Calculations:
Let’s assume the following speeds:
- Bethany: 3 miles per hour
- Morgan: 4 miles per hour
- Taylor: 5 miles per hour

Now we can plug these into the formula.

1. **Bethany:**
\[
\text{Time}_{Bethany} = \frac{6 \text{ miles}}{3 \text{ mph}} = 2 \text{ hours}
\]

2. **Morgan:**
\[
\text{Time}_{Morgan} = \frac{6 \text{ miles}}{4 \text{ mph}} = 1.5 \text{ hours}
\]

3. **Taylor:**
\[
\text{Time}_{Taylor} = \frac{6 \text{ miles}}{5 \text{ mph}} = 1.2 \text{ hours}
\]

### Summary of Times:
- Bethany: 2 hours
- Morgan: 1.5 hours
- Taylor: 1.2 hours

### Conclusion:
From the times calculated, Taylor arrives first, followed by Morgan, and then Bethany.

### Graph:
To visualize this, you can plot a graph with time on the y-axis and each girl on the x-axis. The height of the bars (or points, if plotted differently) represents the time each girl takes to reach the activity center.

If you share the specific speeds, I can provide adjusted calculations and graphs accordingly!