Given information:
Horizontal scale ratio: 1/750
Vertical scale ratio: 1/75
Prototype period: 18 hours

To find:
Model period

Approach:
We know that the model scales are defined as the ratios of corresponding lengths in the model to those in the prototype. Therefore, we can use the scale ratios to find the model period.

Step-by-step explanation:

1. Convert the prototype period to minutes:
The prototype period is given as 18 hours. Since there are 60 minutes in an hour, the prototype period in minutes is:
18 hours × 60 minutes/hour = 1080 minutes

2. Use the scale ratios to find the model period:
The horizontal scale ratio is given as 1/750. This means that 1 unit of length in the model represents 750 units of length in the prototype. Similarly, the vertical scale ratio is given as 1/75, which means that 1 unit of height in the model represents 75 units of height in the prototype.

To find the model period, we need to find the ratio between the time in the model and the time in the prototype. Since time is not affected by scale, the ratio of the model period to the prototype period should be the same as the ratio of the corresponding lengths. Therefore, we can write:

Model period/Prototype period = Horizontal scale ratio/Vertical scale ratio

Substituting the given values:
Model period/1080 minutes = (1/750)/(1/75)

Simplifying the equation:
Model period/1080 minutes = (1/750) × (75/1)
Model period/1080 minutes = 75/750
Model period/1080 minutes = 1/10

Cross-multiplying:
Model period = (1/10) × 1080 minutes
Model period = 108 minutes

3. Convert the model period to hours and minutes:
Since the model period is given in minutes, we can convert it to hours and minutes by dividing by 60:
108 minutes ÷ 60 minutes/hour = 1 hour and 48 minutes

Therefore, the model period is 1 hour and 48 minutes, which corresponds to the option B: 12.47.