A manufacturing plant uses a machine lubricant at a constant rate of 0.08 fluid ounces per… — SAT

A manufacturing plant uses a machine lubricant at a constant rate of $0.08$ fluid ounces per second of operation. The plant operates the machinery for $8$ hours per day, $5$ days a week. The lubricant is purchased in drums, where each drum contains $15$ gallons of lubricant. How many drums of lubricant does the plant use in a period of $5$ weeks? (Note: $1\text{ gallon} = 128\text{ fluid ounces}$ )

Answer: 30 drums

Answer

The plant uses 30 drums of lubricant in 5 weeks.

To find the number of drums, calculate the total seconds of operation: 5 weeks * 5 days/week * 8 hours/day * 3,600 seconds/hour = 720,000 seconds. Multiply this by the consumption rate of 0.08 fluid ounces/second to get 57,600 fluid ounces. Convert this to gallons by dividing by 128 fluid ounces/gallon to get 450 gallons. Finally, divide by 15 gallons/drum to find that 30 drums are used.

Step-by-Step Solution

Calculate the total number of operational seconds in the 5-week period.

720{}000\text{ seconds}

Multiply 5 weeks by 5 days per week, 8 hours per day, and 3,600 seconds per hour:

5 \times 5 \times 8 \times 3{}600 = 720{}000

Calculate the total volume of lubricant used in fluid ounces.

57{}600\text{ fluid ounces}

Multiply the rate of

0.08\text{ fluid ounces per second}

by the total operational seconds:

720{}000 \times 0.08 = 57{}600

Convert the total fluid ounces to gallons.

450\text{ gallons}

Divide the total fluid ounces by the conversion factor of

128\text{ fluid ounces per gallon}

57{}600 / 128 = 450

Calculate the total number of drums needed.

30\text{ drums}

Divide the total gallons by the capacity of a single drum (

15\text{ gallons}

450 / 15 = 30

Key Concept

Multi-step dimensional analysis and unit conversion under compound rates

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