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Zorluk: ZorUnit Rates

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 1515 gallons of fuel during a 44-hour mission while maintaining a constant speed of 4545 miles per hour. (Fuel efficiency in miles per gallon)1212 miles per gallon
  • A base drainage system removes 4,8004,800 gallons of flooded water in 11 hour and 2020 minutes. (Pumping rate in gallons per minute)6060 gallons per minute
  • An automated packaging line produces 315315 field rations every 4545 minutes. (Production rate in rations per hour)420420 rations per hour
  • A backup communications generator consumes 1818 liters of diesel fuel over 2424 hours of continuous operation. (Consumption rate in milliliters per minute)12.512.5 milliliters per minute

Cevap

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.

Adım Adım Çözüm

1
Calculate the fuel efficiency of the supply truck in miles per gallon.
Total distance = 45×4=18045 \times 4 = 180 miles. Unit rate = 180/15=12180 / 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.
2
Calculate the pumping rate of the drainage system in gallons per minute.
Total time = 60+20=8060 + 20 = 80 minutes. Unit rate = 4,800/80=604,800 / 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.
3
Calculate the production rate of the packaging line in rations per hour.
Rate per minute = 315/45=7315 / 45 = 7 rations/min. Rate per hour = 7×60=4207 \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 (6060).
4
Calculate the consumption rate of the generator in milliliters per minute.
Volume = 18×1,000=18,00018 \times 1,000 = 18,000 mL. Time = 24×60=1,44024 \times 60 = 1,440 minutes. Unit rate = 18,000/1,440=12.518,000 / 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.

Anahtar Kavram

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

Unit Rates

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