Final answer:
To determine the length of model cars built by Asharah and Kenya, we apply the scales provided, resulting in Asharah's model being 3 inches and Kenya's being 6 inches long. This demonstrates the importance of understanding mathematical models and principles to accurately convert actual measurements to scaled representations.
Step-by-step explanation:
To find the length of Asharah and Kenya's model cars, we need to apply the concept of scale factor. The process involves using the given scale to convert actual measurements to scale model measurements. Let's solve both problems:
Asharah's Model Car
The scale given is 1/4 inch = 1 foot. To find the length of Asharah's model car, we use the following steps:
- Determine the actual length of the car which is 12 feet.
- Use the scale factor, 1/4 inch per foot, to calculate the model's length: (1/4 inch/foot) × 12 feet = 3 inches.
The length of Asharah's model car is 3 inches.
Kenya's Model Car
The scale given for Kenya's model is 1/2 inch = 1 foot. To calculate the length of his model, follow these steps:
- The actual length of the car remains 12 feet.
- Use the scale factor, 1/2 inch per foot, to find the model's length: (1/2 inch/foot) × 12 feet = 6 inches.
Kenya's model car is 6 inches long.
Understanding the mathematical models and their construction using scientific and mathematical principles are imperative in making accurate scale conversions. This problem is a straightforward application of proportion and scale factor, which only requires multiplication of the scale by the actual measurement to determine the model's size.