A commercial printing press produces 420 color brochures every 15 minutes. If the press op… — ACT

A commercial printing press produces $420$ color brochures every $15$ minutes. If the press operates continuously at this constant rate, how many hours will it take to produce a total of $5,040$ brochures?

A
$0.8$
B
$1.8$
$3$ Answer
D
$12$
E
$180$

Answer

3 hours

The correct answer is 3 hours because the printing press produces 28 brochures per minute (

420 \div 15

). In one hour (60 minutes), it produces 1,680 brochures (

28 \times 60

). To complete 5,040 brochures, it takes

5,040 \div 1,680 = 3

hours.

Step-by-Step Solution

Determine the unit rate per minute.

420 \text{ brochures} \div 15 \text{ minutes} = 28 \text{ brochures per minute}

Finding the unit rate simplifies conversion to hourly production.

Convert the unit rate to an hourly rate.

28 \text{ brochures/minute} \times 60 \text{ minutes/hour} = 1,680 \text{ brochures per hour}

The question asks for the total time in hours.

Calculate the total hours needed to print 5,040 brochures.

5,040 \text{ brochures} \div 1,680 \text{ brochures/hour} = 3 \text{ hours}

Dividing total target quantity by hourly rate yields the required time.

Key Concept

Unit Rates and Multi-Step Proportional Reasoning

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Common Mistakes

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