A military logistics center uses two automated packaging machines to assemble field ration… — Armed Services Vocational Aptitude Battery (ASVAB)

A military logistics center uses two automated packaging machines to assemble field ration kits. Machine A can assemble $450$ kits in $1.5$ hours. Machine B can assemble $90$ kits every $15$ minutes. If both machines operate simultaneously at their respective constant rates, how many total ration kits can they assemble in $4$ hours?

$2,640$ Cevap
B
$1,224$
C
$1,560$
D
$165$

Cevap

They can assemble

2,640

ration kits in

4

hours.

The correct answer is found by standardizing the production rates into hourly unit rates, adding them together, and multiplying by the total time. Machine A produces at

300

kits/hr (

450 \div 1.5

). Machine B produces at

360

kits/hr (

90 \times 4

, since

15

minutes is a quarter of an hour). The combined hourly rate is

660

kits/hr. In

4

hours, they produce

660 \times 4 = 2,640

kits.

Adım Adım Çözüm

Calculate the hourly unit rate for Machine A.

450 \div 1.5 = 300

kits per hour.

To compare and combine rates, both machines must be evaluated using the same unit of time (hours).

Calculate the hourly unit rate for Machine B.

90

kits per

15

minutes is equal to

90 \times 4 = 360

kits per hour.

There are

60

minutes in an hour, which is exactly four

15

-minute segments (

60 \div 15 = 4

). Therefore, multiplying the

15

-minute production rate by

4

gives the hourly rate.

Calculate the combined hourly rate.

300 + 360 = 660

kits per hour.

Since both machines operate simultaneously, their individual hourly rates are added together to find the total combined rate.

Calculate the total kits assembled in

4

hours.

660 \times 4 = 2,640

kits.

Multiply the combined hourly unit rate by the total operating time to find the final production amount.

Anahtar Kavram

Unit Rates

Soru

Cevap

Adım Adım Çözüm

Anahtar Kavram

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