A commercial printing press uses ink at a constant rate of 0.24 liters per minute. The den… — SAT

A commercial printing press uses ink at a constant rate of $0.24$ liters per minute. The density of the ink is $1.2$ grams per milliliter. Given that $1\text{ liter} = 1,000\text{ milliliters}$ and $1\text{ kilogram} = 1,000\text{ grams}$ , how many kilograms of ink does the press use in $8$ hours of continuous operation?

A
$96.00$
B
$115.20$
$138.24$ Answer
D
$2.30$

Answer

The press uses

138.24

kilograms of ink in

8

hours of continuous operation.

To find the mass in kilograms, first convert the

8

hours of operation to minutes:

8 \times 60 = 480\text{ minutes}

. Next, find the volume of ink used in liters:

480 \times 0.24 = 115.2\text{ liters}

. Convert this volume to milliliters:

115.2 \times 1,000 = 115,200\text{ milliliters}

. Using the density of

1.2\text{ grams per milliliter}

, calculate the mass in grams:

115,200 \times 1.2 = 138,240\text{ grams}

. Finally, convert the mass to kilograms:

138,240 \div 1,000 = 138.24\text{ kilograms}

Step-by-Step Solution

Convert the operation time from hours to minutes.

8\text{ hours} \times 60\text{ minutes/hour} = 480\text{ minutes}

Since the ink consumption rate is given in liters per minute, the time must be in minutes to calculate the total volume of ink used.

Calculate the total volume of ink used in liters.

480\text{ minutes} \times 0.24\text{ liters/minute} = 115.2\text{ liters}

Multiply the total operation time by the rate of ink usage to find the total liters of ink consumed.

Convert the volume from liters to milliliters.

115.2\text{ liters} \times 1,000\text{ milliliters/liter} = 115,200\text{ milliliters}

Since the ink density is given in grams per milliliter, the volume must be in milliliters to find the mass.

Calculate the mass of the ink in grams using the density.

115,200\text{ milliliters} \times 1.2\text{ grams/milliliter} = 138,240\text{ grams}

Multiply the volume in milliliters by the density to find the mass in grams.

Convert the mass from grams to kilograms.

138,240\text{ grams} \div 1,000\text{ grams/kilogram} = 138.24\text{ kilograms}

Divide the mass in grams by

1,000

to convert it to kilograms.

Key Concept

Multi-step unit conversion involving rates, volume, density, and mass.

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