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Zorluk: OrtaDirect Proportions

An earth-moving excavator clears 120120 cubic yards of debris in 4545 minutes. Operating at this constant rate, how many cubic yards of debris will the excavator clear in 33 hours?

  1. 480Cevap
  2. B
    8
  3. C
    30
  4. D
    48

Cevap

480
The correct answer is found by first converting 33 hours into 180180 minutes. Then, applying a direct proportion, 12045=x180\frac{120}{45} = \frac{x}{180}, yields x=480x = 480. Alternatively, observing that 180180 minutes is exactly 44 times as long as 4545 minutes means the excavator will clear 44 times the debris: 120×4=480120 \times 4 = 480.

Adım Adım Çözüm

1
Convert the target time from hours to minutes so the units match the given rate.
3 hours×60 minutes/hour=180 minutes3 \text{ hours} \times 60 \text{ minutes/hour} = 180 \text{ minutes}
Units of time must be identical before setting up a valid proportion.
2
Set up a direct proportion relating the volume of debris to the time taken.
12045=x180\frac{120}{45} = \frac{x}{180}
Since the excavator works at a constant rate, the ratio of volume to time remains constant.
3
Solve for the unknown volume (xx) by cross-multiplying or finding a common multiplier.
x=120×18045=120×4=480x = \frac{120 \times 180}{45} = 120 \times 4 = 480
Isolating xx provides the total cubic yards cleared in 180180 minutes.

Anahtar Kavram

Direct proportions with unit conversions
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Direct Proportions

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