A wire manufacturing facility operates 40 extrusion machines simultaneously. Each machine … — Armed Services Vocational Aptitude Battery (ASVAB)

A wire manufacturing facility operates $40$ extrusion machines simultaneously. Each machine produces $15$ centimeters of copper wire per second. How many kilometers of copper wire do all $40$ machines produce combined in exactly one hour?

A
$0.36$
B
$2,160$
$21.6$ Answer
D
$21,600$

Answer

The machines produce a combined total of

21.6

kilometers of copper wire in one hour.

First, find the facility's total production per second by multiplying

40

machines by

15

cm, yielding

600

cm/sec. Next, multiply by

3,600

(the number of seconds in one hour) to find the hourly production in centimeters, which equals

2,160,000

cm. Finally, convert centimeters to kilometers by dividing by

100,000

(

100 \text{ cm} = 1 \text{ m}

and

1,000 \text{ m} = 1 \text{ km}

), resulting in

21.6

kilometers.

Step-by-Step Solution

Calculate the total length of wire produced per second by all machines combined.

40 \times 15 = 600

centimeters per second.

This establishes the facility's baseline production rate before factoring in a longer duration.

Scale the production rate from seconds to hours.

600 \times 3,600 = 2,160,000

centimeters per hour.

There are

60

seconds in a minute and

60

minutes in an hour, meaning there are

3,600

seconds in exactly one hour.

Convert the total length from centimeters to kilometers.

2,160,000 \div 100,000 = 21.6

kilometers.

Since there are

100

centimeters in a meter and

1,000

meters in a kilometer, the total conversion factor is

100,000

centimeters per kilometer.

Key Concept

Multi-step metric prefix conversions involving time rates and combined totals.

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