Question

this question has two parts. first, answer part a. then, answer part b.
part a
lin has a scale model of a modern train. the model is created at a scale of 1 to 48.
the height of the model train is 102 millimeters. what is the actual height of the train in meters?
part b
on the scale model, the distance between the wheels on the left and the wheels on the right is 1 1/4 inches. the state of wyoming has old railroad tracks that are 4.5 feet apart. complete the statements about whether the modern train can travel on those tracks.
the modern train needs tracks that are select choice inches apart. the old tracks are select choice inches, so they select choice wide enough

Explanation:

Part A

Step1: Convert scale ratio to actual size

The scale is \(1:48\), which means the actual size is \(48\) times the model size. The model height is \(102\) millimeters. First, find the actual height in millimeters: \(102\times48 = 4896\) millimeters.

Step2: Convert millimeters to meters

Since \(1\) meter \( = 1000\) millimeters, then \(4896\div1000=4.896\) meters.

Part B

Step1: Convert the distance on the model to actual distance (inches to feet)

The distance between wheels on the model is \(1\frac{1}{4}=\frac{5}{4}\) inches. Using the scale \(1:48\), the actual distance in inches is \(\frac{5}{4}\times48 = 60\) inches.

Step2: Convert inches to feet

Since \(1\) foot \( = 12\) inches, then \(60\div12 = 5\) feet. The old tracks are \(4.5\) feet wide. \(5>4.5\), so the modern train cannot travel on those tracks.

Answer:

Part A

\(4.896\) m

Part B

The modern train cannot travel on those tracks.