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Zorluk: ZorUnit Rates

An aviation maintenance depot uses two automated riveting machines to assemble fuselage panels. Machine A can install 240240 rivets in 44 hours. Machine B can install 3030 rivets every 2020 minutes. If both machines operate simultaneously, how many hours will it take them to install a total of 6,3006,300 rivets?

  1. A
    30
  2. 42Cevap
  3. C
    63
  4. D
    70

Cevap

The correct answer is 42 hours.
To solve this problem, both machine rates must first be converted to the same time unit (hours). Machine A operates at 6060 rivets per hour (240÷4240 \div 4). Machine B operates at 9090 rivets per hour (since there are three 2020-minute periods in an hour, 30×3=9030 \times 3 = 90). Together, they install 150150 rivets per hour (60+9060 + 90). Dividing the total requirement of 6,3006,300 rivets by the combined rate of 150150 rivets per hour yields exactly 4242 hours.

Adım Adım Çözüm

1
Calculate the unit rate for Machine A in rivets per hour.
240 rivets÷4 hours=60 rivets per hour240 \text{ rivets} \div 4 \text{ hours} = 60 \text{ rivets per hour}
To combine the rates of both machines, they must be in the same unit of measure (rivets per hour).
2
Calculate the unit rate for Machine B in rivets per hour.
30 rivets÷20 minutes=1.5 rivets per minute30 \text{ rivets} \div 20 \text{ minutes} = 1.5 \text{ rivets per minute}. 1.5×60=90 rivets per hour1.5 \times 60 = 90 \text{ rivets per hour}
Machine B's rate is given per 2020 minutes, so it must be scaled up to an hourly rate by multiplying by 6060 minutes.
3
Calculate the combined hourly rate of both machines.
60+90=150 rivets per hour60 + 90 = 150 \text{ rivets per hour}
The machines operate simultaneously, so their individual hourly rates are added together.
4
Determine the total time required to install 6,3006,300 rivets.
6,300 rivets÷150 rivets per hour=42 hours6,300 \text{ rivets} \div 150 \text{ rivets per hour} = 42 \text{ hours}
Dividing the total work required by the combined hourly rate gives the total time needed.

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