An industrial water filtration system filters water at a constant rate of 0.5\text{ liters… — SAT

An industrial water filtration system filters water at a constant rate of $0.5\text{ liters per second}$ . The system consumes a chemical powder at a rate of $2.5\text{ milligrams}$ per gram of impurities removed from the water. If the water contains an average of $0.12\text{ grams}$ of impurities per liter, how many grams of the chemical powder does the system consume during $4\text{ hours}$ of continuous operation?

Answer: 2.16 grams

Answer

The system consumes

2.16\text{ grams}

of chemical powder during the

4

hours of operation.

The correct answer is

2.16

. First, convert the

4

hours of continuous operation into seconds:

4 \times 3,600 = 14,400

seconds. Next, multiply this duration by the filtration rate to find the total water filtered:

14,400 \times 0.5 = 7,200

liters. Multiply the volume by the impurity concentration to find the total mass of impurities:

7,200 \times 0.12 = 864

grams. Then, find the mass of chemical powder consumed:

864 \times 2.5 = 2,160

milligrams. Finally, convert milligrams to grams by dividing by

1,000

, resulting in

2.16

grams.

Step-by-Step Solution

Convert the operating time from hours to seconds.

14,400\text{ seconds}

Since the filtration rate is given in liters per second, the total operating time must be converted from hours to seconds to align units. There are

3,600

seconds in one hour.

Calculate the total volume of water filtered during the operation.

7,200\text{ liters}

Multiply the operating time in seconds by the filtration rate of

0.5

liters per second.

Calculate the total mass of impurities removed from the filtered water.

864\text{ grams}

Multiply the total volume of filtered water by the concentration rate of

0.12

grams of impurities per liter.

Determine the mass of chemical powder consumed in milligrams.

2,160\text{ milligrams}

Multiply the total mass of impurities in grams by the consumption rate of

2.5

milligrams of chemical powder per gram of impurities.

Convert the mass of chemical powder from milligrams to grams.

2.16\text{ grams}

Divide the mass in milligrams by

1,000

because there are

1,000

milligrams in one gram.

Key Concept

Dimensional analysis and multi-step unit conversion involving rates

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