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A cargo ship travels at a constant speed of 24 knots24\text{ knots}. The ship's engine consumes fuel at a constant rate of 23 liters per minute23\text{ liters per minute}. The fuel has a density of 0.80 grams per milliliter0.80\text{ grams per milliliter}. Given that 1 knot=1.15 miles per hour1\text{ knot} = 1.15\text{ miles per hour} and 1 metric ton=1,000 kilograms1\text{ metric ton} = 1,000\text{ kilograms}, what is the ship's fuel consumption rate in metric tons per mile?

  1. 0.04Cevap
  2. B
    0.053
  3. C
    0.0625
  4. D
    0.40

Cevap

0.04
The correct answer is obtained by first converting the ship's speed to miles per hour (24×1.15=27.6 mph24 \times 1.15 = 27.6\text{ mph}). Next, the fuel usage is converted to liters per hour (23×60=1,380 L/hr23 \times 60 = 1,380\text{ L/hr}). Using the density conversion where 0.80 g/mL0.80\text{ g/mL} is equal to 0.80 kg/L0.80\text{ kg/L}, the fuel consumption is converted to mass (1,380×0.80=1,104 kg/hr1,380 \times 0.80 = 1,104\text{ kg/hr}), which is equivalent to 1.1041.104 metric tons per hour. Finally, dividing the fuel rate by the speed gives the rate per mile: 1.104/27.6=0.041.104 / 27.6 = 0.04 metric tons per mile.

Adım Adım Çözüm

1
Convert the speed of the cargo ship from knots to miles per hour.
24 knots×1.15 miles per hour per knot=27.6 miles per hour24\text{ knots} \times 1.15\text{ miles per hour per knot} = 27.6\text{ miles per hour}
To match the final unit of miles, we convert knots to miles per hour.
2
Convert the fuel consumption rate from liters per minute to liters per hour.
23 liters/minute×60 minutes/hour=1,380 liters/hour23\text{ liters/minute} \times 60\text{ minutes/hour} = 1,380\text{ liters/hour}
Since speed is in miles per hour, we convert the fuel consumption to a per-hour rate.
3
Convert the volume consumption rate to a mass consumption rate using the density.
1,380 liters/hour×0.80 kilograms/liter=1,104 kilograms/hour1,380\text{ liters/hour} \times 0.80\text{ kilograms/liter} = 1,104\text{ kilograms/hour}
Density of 0.80 g/mL0.80\text{ g/mL} is equivalent to 0.80 kg/L0.80\text{ kg/L} because there are 1,0001,000 grams in a kilogram and 1,0001,000 milliliters in a liter.
4
Convert the mass rate from kilograms per hour to metric tons per hour.
1,104 kilograms/hour1,000 kilograms/metric ton=1.104 metric tons/hour\frac{1,104\text{ kilograms/hour}}{1,000\text{ kilograms/metric ton}} = 1.104\text{ metric tons/hour}
To match the final unit of metric tons, we divide the kilograms by 1,0001,000.
5
Calculate the fuel consumption rate in metric tons per mile by dividing the hourly fuel consumption by the hourly speed.
1.104 metric tons/hour27.6 miles/hour=0.04 metric tons/mile\frac{1.104\text{ metric tons/hour}}{27.6\text{ miles/hour}} = 0.04\text{ metric tons/mile}
Dividing the rate of fuel consumed per hour by the distance traveled per hour gives the fuel consumed per mile.

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Unit conversions with compound rates and density scaling
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