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Difficulty: HardDirect Proportions

An industrial textile loom weaves 4.54.5 yards of heavy canvas every 1212 minutes. Operating at this same constant rate, how many feet of canvas will the loom produce during a complete 88-hour work shift?

Answer: 540 feet

Answer

540 feet
To solve this problem, you must properly scale a direct proportion while paying careful attention to units. First, harmonize the time units: an 8-hour shift is equal to 480 minutes (8 × 60). Next, set up a proportion or find the scale factor: 480 minutes is exactly 40 times longer than the 12-minute baseline (480 ÷ 12 = 40). Because the loom operates at a constant rate, it will produce 40 times as much canvas. Multiply the 4.5 yards by 40 to find the total yards produced (4.5 × 40 = 180 yards). Finally, the question asks for the answer in feet. Since there are 3 feet in 1 yard, multiply 180 yards by 3 to get exactly 540 feet.

Step-by-Step Solution

1
Convert the total operating time from hours to minutes to match the given rate's unit of time.
8 hours×60 minutes/hour=480 minutes8 \text{ hours} \times 60 \text{ minutes/hour} = 480 \text{ minutes}
Units of time must be identical before calculating the direct proportion.
2
Determine how many 12-minute intervals occur in the 480-minute shift.
480÷12=40 intervals480 \div 12 = 40 \text{ intervals}
This establishes the multiplier (scale factor) that will be applied to the fabric production.
3
Calculate the total yards of canvas produced during the entire shift.
40×4.5 yards=180 yards40 \times 4.5 \text{ yards} = 180 \text{ yards}
Because production is directly proportional to time, multiplying the base production by the time scale factor yields total yards.
4
Convert the total production from yards to feet to answer the specific question asked.
180 yards×3 feet/yard=540 feet180 \text{ yards} \times 3 \text{ feet/yard} = 540 \text{ feet}
The stem explicitly asks for the final length in feet, making this unit conversion a critical final step.

Key Concept

Solving multi-step direct proportion problems that require initial and final unit harmonizations (time and length).
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Topics

Direct Proportions

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