A park director is planning a new 3 \frac{1}{2}-mile nature trail. The first segment of th… — Armed Services Vocational Aptitude Battery (ASVAB)

A park director is planning a new $3 \frac{1}{2}$ -mile nature trail. The first segment of the trail is a dirt path that covers exactly $1 \frac{1}{4}$ miles. The second segment consists of $1,500$ yards of crushed gravel. The final segment is a continuous wooden boardwalk leading back to the visitor center. What is the length of the wooden boardwalk in feet?

$7,380$ Answer
B
$6,060$
C
$11,380$
D
$10,380$

Answer

The wooden boardwalk is

7,380

feet long.

To find the missing segment, all given measurements must be converted to a common unit (feet). A length of

3 \frac{1}{2}

miles is equal to

18,480

feet,

1 \frac{1}{4}

miles is equal to

6,600

feet, and

1,500

yards is equal to

4,500

feet. Subtracting the two known segments (

6,600 + 4,500 = 11,100

feet) from the total (

18,480

feet) yields the final segment length of

7,380

feet.

Step-by-Step Solution

Convert the total length of the trail from miles to feet.

3 \frac{1}{2} \times 5,280 = 18,480

feet

Because the final answer must be in feet, it is best to establish the total boundary constraint in the target unit.

Convert the length of the dirt path from miles to feet.

1 \frac{1}{4} \times 5,280 = 6,600

feet

All segments must be in the same unit to perform addition and subtraction.

Convert the length of the crushed gravel segment from yards to feet.

1,500 \times 3 = 4,500

feet

There are

3

feet in

1

yard, so multiplying yards by

3

gives the measurement in feet.

Subtract the lengths of the first two segments from the total trail length to find the boardwalk length.

18,480 - (6,600 + 4,500) = 18,480 - 11,100 = 7,380

feet

The trail consists of three contiguous parts, so removing the known parts from the whole leaves the unknown final part.

Key Concept

Multi-step conversion of standard US Customary linear units (miles and yards) to a common base unit (feet) to solve for an unknown segment.

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