Match each military logistical operation to its correct unit rate. Pay close attention to … — Armed Services Vocational Aptitude Battery (ASVAB)

Match each military logistical operation to its correct unit rate. Pay close attention to the requested units of measurement and necessary conversions.

A supply truck uses $15$ gallons of fuel during a $4$ -hour mission while maintaining a constant speed of $45$ miles per hour. (Fuel efficiency in miles per gallon) $12$ miles per gallon
A base drainage system removes $4,800$ gallons of flooded water in $1$ hour and $20$ minutes. (Pumping rate in gallons per minute) $60$ gallons per minute
An automated packaging line produces $315$ field rations every $45$ minutes. (Production rate in rations per hour) $420$ rations per hour
A backup communications generator consumes $18$ liters of diesel fuel over $24$ hours of continuous operation. (Consumption rate in milliliters per minute) $12.5$ milliliters per minute

Answer

The correct matches are: Supply truck with 12 miles per gallon, Drainage system with 60 gallons per minute, Packaging line with 420 rations per hour, and Generator with 12.5 milliliters per minute.

Each scenario requires identifying the total quantity of the numerator (miles, gallons, rations, milliliters) and dividing it by the corresponding total of the denominator (gallons, minutes, hours). In every case, this necessitates at least one preliminary conversion or calculation step.

Step-by-Step Solution

Calculate the fuel efficiency of the supply truck in miles per gallon.

Total distance =

45 \times 4 = 180

miles. Unit rate =

180 / 15 = 12

miles per gallon.

The fuel efficiency is found by dividing the total distance traveled by the total gallons of fuel consumed, requiring a preliminary distance calculation.

Calculate the pumping rate of the drainage system in gallons per minute.

Total time =

60 + 20 = 80

minutes. Unit rate =

4,800 / 80 = 60

gallons per minute.

The units requested are gallons per minute, so the total time must first be completely converted into minutes before dividing the volume.

Calculate the production rate of the packaging line in rations per hour.

Rate per minute =

315 / 45 = 7

rations/min. Rate per hour =

7 \times 60 = 420

rations per hour.

To find the hourly rate from a minute-based rate, first find the rate per minute, then scale it up by multiplying by the number of minutes in an hour (

60

Calculate the consumption rate of the generator in milliliters per minute.

Volume =

18 \times 1,000 = 18,000

mL. Time =

24 \times 60 = 1,440

minutes. Unit rate =

18,000 / 1,440 = 12.5

mL/min.

Both given quantities require unit conversions (liters to milliliters, and hours to minutes) before performing the final division to find the required rate.

Key Concept

Calculating unit rates involving multi-step operations and dimensional analysis (unit conversions).

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