Find the scale factor from the given story problem. \( \begin{array}{l}\text { (2pts.) } 5 \text {. A model of a locomotive is } 3 \text { incheslong. The actual locomotive is } 18 \text { feet long. What is the scale factor of } \\ \text { the model to the actual locomotive? ( } 12 \text { inches }=1 \text { foot) }\end{array} \)

To find the scale factor, first, convert the actual length of the locomotive from feet to inches. Since there are 12 inches in a foot, the actual locomotive's length is \(18 \text{ feet} \times 12 \text{ inches/foot} = 216 \text{ inches}\). Now, the model is 3 inches long, so the scale factor is the ratio of the model length to the actual length: \[ \text{Scale Factor} = \frac{\text{Model Length}}{\text{Actual Length}} = \frac{3 \text{ inches}}{216 \text{ inches}} = \frac{1}{72}. \] So, the scale factor of the model to the actual locomotive is \( \frac{1}{72} \). In simpler terms, one inch on the model represents 72 inches (or 6 feet) in real life. That's quite a fascinating way to visualize how much smaller the model is compared to the actual locomotive!