A specialized laser cutter cuts steel sheet metal at a constant rate of 18 inches per minu… — SAT

A specialized laser cutter cuts steel sheet metal at a constant rate of $18$ inches per minute. At this rate, how many seconds does it take the laser cutter to cut a length of $6$ feet of steel? ( $1\text{ foot} = 12\text{ inches}$ )

Answer: 240 seconds

Answer

The correct answer is 240.

To find the number of seconds it takes the laser cutter to cut

6

feet of steel, we first convert the length to inches:

6\text{ feet} \times 12\text{ inches/foot} = 72\text{ inches}

. Next, we divide this length by the cutting rate to find the duration in minutes:

72\text{ inches} \div 18\text{ inches/minute} = 4\text{ minutes}

. Finally, we convert the minutes into seconds: $4\text{ minutes} \times 60\text{ seconds/minute} = 240\text{ seconds}.

Step-by-Step Solution

Convert the total cutting distance from feet to inches.

72\text{ inches}

Since the rate is given in inches per minute, we must convert the length from feet to inches to align the units. Knowing that

1\text{ foot} = 12\text{ inches}

, we multiply

6

12

Calculate the time in minutes to cut

72\text{ inches}

at a rate of

18\text{ inches/minute}

4\text{ minutes}

Dividing the total distance (

72\text{ inches}

) by the cutting rate (

18\text{ inches/minute}

) yields the time in minutes.

Convert the time from minutes to seconds.

240\text{ seconds}

Since

1\text{ minute} = 60\text{ seconds}

, multiplying

4

minutes by

60

gives the final time in seconds.

Key Concept

Performing multi-step unit conversions using rate and dimensional analysis.

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