A construction crew has a spool containing exactly \frac{1}{4} mile of underground cable. … — Armed Services Vocational Aptitude Battery (ASVAB)

A construction crew has a spool containing exactly $\frac{1}{4}$ mile of underground cable. They use $120 \frac{2}{3}$ yards of the cable for their first trench and $412$ feet $8$ inches of the cable for their second trench. How much cable remains on the spool?

545 feet 4 inchesAnswer
B
450 feet
C
786 feet 8 inches
D
545 feet 2 inches

Answer

545 feet 4 inches

To find the remaining cable, all measurements must be converted to a common unit. First, find the total cable in feet: since

1 \text{ mile} = 5280 \text{ feet}

\frac{1}{4} \text{ mile} = 1320 \text{ feet}

. Next, convert the first trench length to feet:

120 \frac{2}{3} \text{ yards} \times 3 \text{ feet/yard} = 362 \text{ feet}

. The second trench is

412 \text{ feet } 8 \text{ inches}

. The total used is

362 \text{ feet} + 412 \text{ feet } 8 \text{ inches} = 774 \text{ feet } 8 \text{ inches}

. Finally, subtract this from the starting amount. Borrowing

1 \text{ foot}

(

12 \text{ inches}

) from

1320 \text{ feet}

gives

1319 \text{ feet } 12 \text{ inches}

. Subtracting the used cable gives

1319 - 774 = 545 \text{ feet}

and

12 - 8 = 4 \text{ inches}

Step-by-Step Solution

Convert the total cable length from miles to feet.

\frac{1}{4} \times 5280 = 1320

feet.

Standardizing all measurements to the same base unit (feet) is required before adding or subtracting.

Convert the length used for the first trench from yards to feet.

120 \frac{2}{3} \times 3 = 362

feet.

There are 3 feet in a yard, so multiplying the mixed fraction by 3 gives the exact length in feet.

Calculate the total amount of cable used for both trenches.

362 \text{ feet} + 412 \text{ feet } 8 \text{ inches} = 774 \text{ feet } 8 \text{ inches}

Adding the individual segments provides the total length that must be subtracted from the spool.

Subtract the total used cable from the total spool length.

1320 \text{ feet} - 774 \text{ feet } 8 \text{ inches} = 545 \text{ feet } 4 \text{ inches}

To subtract the 8 inches, borrow 1 foot (12 inches) from 1320 feet to make it 1319 feet 12 inches. Subtracting yields

1319 - 774 = 545

feet and

12 - 8 = 4

inches.

Key Concept

Multi-step conversion and arithmetic using US Customary linear measurements

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