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Difficulty: MediumDirect Proportions

A commercial 3D printer extrudes 1.21.2 kilograms of plastic filament every 4545 minutes of operation. Assuming the printer continues to operate at this exact constant rate, how many grams of filament will it extrude during a 33-hour continuous printing session?

  1. A
    4.84.8
  2. B
    8080
  3. C
    300300
  4. 48004800Answer

Answer

The printer will extrude 4800 grams of filament.
Solving this requires maintaining consistent units while scaling up the operation time. Converting the 3-hour print session into 180 minutes reveals that the printer operates for exactly 4 times the duration of the baseline 45-minute period (180 divided by 45 is 4). Because the relationship is a direct proportion, the mass of filament used also scales by a factor of 4. Multiplying 1.2 kilograms by 4 yields 4.8 kilograms. Finally, converting 4.8 kilograms into grams by multiplying by 1000 gives 4800 grams.

Step-by-Step Solution

1
Convert the target time period from hours to minutes to match the units of the given rate.
3 hours=3×60=180 minutes3 \text{ hours} = 3 \times 60 = 180 \text{ minutes}
Units must be consistent across the proportion equation to find the correct multiplier.
2
Set up a direct proportion to find the amount of filament extruded in kilograms over the new time period.
1.2 kg45 min=x kg180 min⇒x=1.2×(18045)=1.2×4=4.8 kg\frac{1.2 \text{ kg}}{45 \text{ min}} = \frac{x \text{ kg}}{180 \text{ min}} \Rightarrow x = 1.2 \times \left(\frac{180}{45}\right) = 1.2 \times 4 = 4.8 \text{ kg}
The mass of filament extruded scales directly with the time the machine operates.
3
Convert the resulting mass from kilograms to grams.
4.8 kg=4.8×1000=4800 grams4.8 \text{ kg} = 4.8 \times 1000 = 4800 \text{ grams}
The question specifically asks for the final answer in grams.

Key Concept

Direct Proportions with Unit Conversions
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Topics

Direct Proportions

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