An industrial printing press uses ink at a constant rate of 0.05 milliliters per square ce… — SAT

An industrial printing press uses ink at a constant rate of $0.05$ milliliters per square centimeter of printed paper. The press prints a continuous roll of paper that is $40$ centimeters wide at a constant speed of $2$ meters per second. At this rate, how many liters of ink does the press use during $1$ hour of continuous printing?

Answer: 1440 liters

Answer

1440

The correct answer is 1440. First, convert the speed of the paper from meters per second to centimeters per second:

2 \text{ m/s} \times 100 \text{ cm/m} = 200 \text{ cm/s}

. Next, find the rate at which the paper surface area is printed:

40 \text{ cm} \times 200 \text{ cm/s} = 8,000 \text{ cm}^2/\text{s}

. Multiply this by the ink usage rate to find milliliters of ink per second:

8,000 \text{ cm}^2/\text{s} \times 0.05 \text{ mL/cm}^2 = 400 \text{ mL/s}

. Since there are

3,600

seconds in

1

hour, the press uses

400 \text{ mL/s} \times 3,600 \text{ s} = 1,440,000 \text{ mL}

of ink per hour. Finally, convert milliliters to liters:

1,440,000 \text{ mL} \div 1,000 \text{ mL/L} = 1,440

liters.

Step-by-Step Solution

Convert the speed of the paper from meters per second to centimeters per second.

200 \text{ cm/s}

To align the speed unit with the paper width unit (

40 \text{ cm}

Calculate the surface area of paper printed per second.

8,000 \text{ cm}^2/\text{s}

Multiply the width of the paper (

40 \text{ cm}

) by the converted speed (

200 \text{ cm/s}

Calculate the volume of ink used per second in milliliters.

400 \text{ mL/s}

Multiply the area printed per second (

8,000 \text{ cm}^2/\text{s}

) by the ink consumption rate (

0.05 \text{ mL/cm}^2

Convert the ink volume rate from per second to per hour.

1,440,000 \text{ mL/h}

Multiply the rate per second by

3,600

, since there are

3,600

seconds in

1

hour.

Convert the final volume from milliliters to liters.

1440

Divide the total milliliters (

1,440,000

) by

1,000

, since

1

liter is equal to

1,000

milliliters.

Key Concept

Multi-step dimensional analysis and compound unit conversion (length, area, volume, and time).

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