To determine the number of passenger stops [tex]\( p \)[/tex] that Mr. Martin had on Tuesday, let's break down the problem step-by-step.
1. Understand the problem statement:
- Without any stops, Mr. Martin takes 12 minutes to complete his route.
- Each passenger stop adds 30 seconds to his travel time. Note that 30 seconds is equal to 0.5 minutes.
- On Tuesday, his total travel time was 14 minutes.
2. Set up the equation:
- Let's use [tex]\( p \)[/tex] to denote the number of passenger stops.
- The total time spent, which is 14 minutes, includes the 12 minutes of driving without stopping plus the time added for stopping to pick up passengers.
- If each stop adds 0.5 minutes, the total time added by [tex]\( p \)[/tex] stops is [tex]\( 0.5p \)[/tex] minutes.
3. Formulate the equation:
- The total time he traveled on Tuesday can be represented as the sum of his base travel time and the additional time for stops:
[tex]\[
14 = 12 + 0.5p
\][/tex]
4. Identify the correct equation:
- Comparing this equation with the given options:
[tex]\[
\boxed{14 = 0.5p + 12}
\][/tex]
This equation correctly reflects the relationship between the total travel time (14 minutes), the base travel time (12 minutes), and the additional time due to the number of stops (0.5 minutes per stop).
Therefore, the correct equation to determine the number of passenger stops [tex]\( p \)[/tex] Mr. Martin made on Tuesday is:
[tex]\[ 14 = 0.5p + 12 \][/tex]
