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Question

Difficulty: MediumDirect Proportions

A shipyard fabricator welds 3030 inches of steel seam every 1515 minutes. Operating at this exact constant rate, how many feet of steel seam will the fabricator weld in a 66-hour shift?

  1. A
    15
  2. 60Answer
  3. C
    720
  4. D
    8,640

Answer

60
The correct answer is derived by first converting the 6-hour shift to 360 minutes. Setting up the direct proportion yields a total of 720 inches (30×360÷1530 \times 360 \div 15). Finally, dividing by 12 correctly converts the length into 60 feet.

Step-by-Step Solution

1
Harmonize the time units by converting the 6-hour shift into minutes.
6 hours×60 minutes/hour=360 minutes6 \text{ hours} \times 60 \text{ minutes/hour} = 360 \text{ minutes}
The given rate is in minutes, so the total operational time must also be in minutes to set up a valid proportion.
2
Set up a direct proportion or find the unit rate of welding.
30 inches15 minutes=2 inches per minute\frac{30 \text{ inches}}{15 \text{ minutes}} = 2 \text{ inches per minute}
Determining the rate per minute simplifies the calculation for the entire shift.
3
Calculate the total length of seam welded in inches.
2 inches/minute×360 minutes=720 inches2 \text{ inches/minute} \times 360 \text{ minutes} = 720 \text{ inches}
Applying the constant rate to the total operational time yields the total production in the initial unit.
4
Convert the total inches into the requested unit of feet.
720 inches÷12 inches/foot=60 feet720 \text{ inches} \div 12 \text{ inches/foot} = 60 \text{ feet}
The question explicitly asks for the final answer in feet, requiring a unit conversion.

Key Concept

Direct proportions with unit conversion
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Topics

Direct Proportions

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