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Difficulty: EasyDirect Proportions

A portable generator consumes 88 liters of fuel every 1212 hours of operation. At this constant rate, how many liters of fuel will the generator consume in 4848 hours of operation?

  1. A
    2
  2. B
    3.2
  3. 32Answer
  4. D
    72

Answer

The generator will consume 32 liters of fuel.
Because the generator operates at a constant rate, the relationship between time and fuel is a direct proportion. The new operating time (4848 hours) is exactly 44 times longer than the original operating time (1212 hours). Therefore, the fuel consumption will also be 44 times greater: 8 liters×4=32 liters8 \text{ liters} \times 4 = 32 \text{ liters}.

Step-by-Step Solution

1
Determine the relationship between the two operating times.
48÷12=448 \div 12 = 4
Finding the scale factor makes it simple to calculate the proportionally larger amount of fuel.
2
Multiply the original fuel amount by the scale factor.
8×4=328 \times 4 = 32 liters
In a direct proportion, whatever factor scales the time must also scale the fuel consumption.

Key Concept

Direct proportions state that as one quantity increases by a certain multiplier, the related quantity increases by that exact same multiplier.
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Topics

Direct Proportions

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