A machine at a factory seals 15 boxes every 4 minutes. At this rate, how many minutes will… — ACT

A machine at a factory seals $15$ boxes every $4$ minutes. At this rate, how many minutes will it take the machine to seal $90$ boxes?

The correct answer is

24

minutes. Since the machine seals

15

boxes every

4

minutes, sealing

90

boxes requires

6

times the number of boxes, which will take

6

times as long:

6 \times 4 = 24

minutes.

The correct answer is

24

. At a constant rate, the ratio of boxes sealed to time remains equivalent. Setting up the proportion

\frac{15}{4} = \frac{90}{x}

and cross-multiplying gives

15x = 360

, which simplifies to

x = 24

. Alternatively, since

90

boxes is

6

times the initial amount of

15

boxes (

90 \div 15 = 6

), the time required must also be

6

times the initial time:

6 \times 4 = 24

minutes.

Determine the scaling factor for the number of boxes.

Scaling factor is

6

Divide the target number of boxes by the initial rate's number of boxes:

90 \div 15 = 6

Multiply the time interval by the scaling factor to find the total time required.

24

minutes.

Multiply the

4

minutes per interval by the scaling factor of

6

6 \times 4 = 24

Solving direct proportion problems by finding equivalent rates.

Find the unit rate first: the machine seals

\frac{15}{4} = 3.75

boxes per minute. To find the time to seal

90

boxes, divide the total boxes by the unit rate:

\frac{90}{3.75} = 24

minutes.

Estimated Time:45s

Question