A hobbyist is building a scale model of a historic steam locomotive using a scale of 1:48.… — Armed Services Vocational Aptitude Battery (ASVAB)

A hobbyist is building a scale model of a historic steam locomotive using a scale of $1:48$ . If the actual locomotive is $60\text{ feet}$ long, what is the length of the model locomotive in inches?

Answer: 15 inches

Answer

To find the length of the scale model, the actual length of the locomotive must first be converted into inches. Since there are

12\text{ inches}

in a foot,

60\text{ feet}

is equal to

720\text{ inches}

. Using the scale ratio of

1:48

, divide the actual length in inches by

48

to find the model's length. Calculating

720 \div 48

yields a model length of

15\text{ inches}

Step-by-Step Solution

Convert the actual length of the locomotive from feet to inches.

60 \times 12 = 720\text{ inches}

The question asks for the model length in inches, so it is necessary to match the units before applying the scale factor.

Calculate the model length using the

1:48

scale ratio.

720 \div 48 = 15\text{ inches}

The scale

1:48

means the model is

48

times smaller than the actual object.

Key Concept

Applying scale ratios across different units of measurement.

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