A military engineering unit is laying communication cable between two outposts. The total … — Armed Services Vocational Aptitude Battery (ASVAB)

A military engineering unit is laying communication cable between two outposts. The total required distance for the connection is $4.5 \text{ miles}$ . The supply depot issues this specific cable in standard spools containing $500 \text{ meters}$ of cable each. If $1 \text{ mile}$ is approximately equal to $1.6 \text{ kilometers}$ , what is the minimum number of spools the unit must request to ensure they have enough cable to cover the entire distance?

A
6
B
9
15Answer
D
144

Answer

To find the total number of spools needed, first unify the units of measurement. Convert 4.5 miles into kilometers by multiplying by 1.6, yielding 7.2 kilometers. Since the spools are measured in meters, convert 7.2 kilometers into meters by multiplying by 1,000, which equals 7,200 meters. Next, divide the 7,200-meter total distance by the 500 meters contained on each spool, resulting in 14.4 spools. Because a fraction of a spool cannot be requested and the full distance must be covered, the number must be rounded up to the nearest whole spool, making 15 the correct amount to request.

Step-by-Step Solution

Convert the total distance from miles to kilometers using the given conversion factor.

4.5 \text{ miles} \times 1.6 \text{ km/mile} = 7.2 \text{ kilometers}

To standardize the units, the distance must first be brought into the metric system where the spool length is measured.

Convert the distance from kilometers to meters.

7.2 \text{ km} \times 1,000 \text{ m/km} = 7,200 \text{ meters}

The spools are measured in meters, so the total distance required must match this unit.

Determine the exact number of spools required by dividing the total meters by the meters per spool.

7,200 \text{ meters} \div 500 \text{ meters/spool} = 14.4 \text{ spools}

This finds how many 500-meter increments are needed to cover the 7,200-meter distance.

Round up to the nearest whole number.

15 \text{ spools}

Since the unit cannot be issued a fraction of a spool and 14 spools would leave them short of the required distance, they must request the next whole number.

Key Concept

Converting across measurement systems (US Customary to Metric) and solving practical constraints using the ceiling function.

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