A naval architect creates a scale drawing for a new submarine. The drawing uses a scale of… — Armed Services Vocational Aptitude Battery (ASVAB)

A naval architect creates a scale drawing for a new submarine. The drawing uses a scale of $\frac{3}{16}\text{ inch} = 15\text{ feet}$ . If the pressure hull measures $4\frac{1}{8}\text{ inches}$ long on the drawing, what is the actual length, in feet, of the pressure hull?

Answer: 330 feet

Answer

330

The scale establishes that every inch on the drawing represents

80

actual feet (

15 \div \frac{3}{16} = 80

). Multiplying the drawing length of

4\frac{1}{8}

inches (or

\frac{33}{8}

inches) by

80

feet per inch yields the correct actual length of

330

feet.

Step-by-Step Solution

Find the unit rate for

1\text{ inch}

of the drawing.

15 \div \frac{3}{16} = 15 \times \frac{16}{3} = 5 \times 16 = 80\text{ feet}

per inch.

Establishing a unit rate simplifies finding actual dimensions for any measurement on the scale drawing.

Convert the drawing measurement from a mixed number to an improper fraction.

4\frac{1}{8} = \frac{4 \times 8 + 1}{8} = \frac{33}{8}\text{ inches}

Improper fractions are required to properly multiply the scale factor with the drawing measurement.

Calculate the actual length by multiplying the map measurement by the unit rate.

\frac{33}{8} \times 80 = 33 \times 10 = 330\text{ feet}

Multiplying the measurement on the drawing by the actual distance per inch yields the total actual distance.

Key Concept

Scale Drawings and Map Measurements

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