Let's carefully break down the problem to determine the correct equation.
1. Identify the base driving time:
- Mr. Martin takes 12 minutes to drive his bus route without stopping.
2. Understand the additional time per stop:
- Each passenger stop adds 30 seconds, which converts to 0.5 minutes (since [tex]\( \frac{30}{60} = 0.5 \)[/tex] minutes).
3. Incorporate the total driving time:
- On Tuesday, Mr. Martin's total driving time is 14 minutes.
We need an equation that relates the total driving time, the base driving time, and the time added for each stop to the number of passenger stops [tex]\( p \)[/tex].
4. Formulate the equation:
- The total driving time is equal to the base driving time plus the additional time for all stops. This can be written as:
[tex]\[ \text{Total time} = \text{Base time} + \text{Time per stop} \times \text{Number of stops (} p \text{)} \][/tex]
5. Substitute the values into the equation:
- The total time (14 minutes) = Base time (12 minutes) + Time per stop (0.5 minutes) * Number of stops ([tex]\( p \)[/tex])
This gives us the equation:
[tex]\[ 14 = 12 + 0.5p \][/tex]
Simplified into a standard form, this can be written as:
[tex]\[ 14 = 0.5p + 12 \][/tex]
So, the correct equation that can be used to determine the number of passenger stops, [tex]\( p \)[/tex], Mr. Martin had on Tuesday is:
[tex]\[ 14 = 0.5p + 12 \][/tex]
Thus, the correct choice from the given options is:
[tex]\[ \boxed{14 = 0.5p + 12} \][/tex]
