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Zorluk: OrtaUnit Conversions

A paper mill machine produces paper at a constant rate of 2424 square feet per second. If 1 square yard=9 square feet1\text{ square yard} = 9\text{ square feet}, how many square yards of paper does the machine produce in 1515 minutes?

  1. A
    40
  2. 2,400Cevap
  3. C
    21,600
  4. D
    194,400

Cevap

2,400
The correct answer of 2,400 is found by first converting the time of 15 minutes to seconds: 15×60=90015 \times 60 = 900 seconds. Next, calculate the total area produced in square feet by multiplying the production rate by the time: 24×900=21,60024 \times 900 = 21,600 square feet. Finally, convert this area to square yards by dividing by 9: 21,600/9=2,40021,600 / 9 = 2,400 square yards.

Adım Adım Çözüm

1
Convert the time from minutes to seconds.
15 minutes×60 seconds/minute=900 seconds15\text{ minutes} \times 60\text{ seconds/minute} = 900\text{ seconds}
The production rate is given in square feet per second, so the time duration must be in seconds.
2
Calculate the total area of paper produced in square feet.
24 square feet/second×900 seconds=21,600 square feet24\text{ square feet/second} \times 900\text{ seconds} = 21,600\text{ square feet}
Multiplying the rate by the total time gives the total amount produced in square feet.
3
Convert the total area from square feet to square yards.
21,600 square feet÷9 square feet/square yard=2,400 square yards21,600\text{ square feet} \div 9\text{ square feet/square yard} = 2,400\text{ square yards}
Since 1 square yard=9 square feet1\text{ square yard} = 9\text{ square feet}, dividing the total square feet by 9 converts the value to square yards.

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Multi-step unit conversions involving rates of change and area scaling.
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