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Question

Difficulty: EasyDirect Proportions

A supply pump transfers 1010 gallons of aviation fuel every 1515 seconds. At this rate, how many gallons of fuel will it transfer in 33 minutes?

  1. 120Answer
  2. B
    270
  3. C
    12
  4. D
    2

Answer

120
The problem establishes a constant rate, which requires a direct proportion to solve. First, convert the 33-minute time period into 180180 seconds to match the units of the given rate. Then, set up the proportion 1015=x180\frac{10}{15} = \frac{x}{180}. Cross-multiplying 1010 by 180180 yields 18001800, and dividing that product by 1515 results in 120120 gallons.

Step-by-Step Solution

1
Harmonize the time units by converting minutes to seconds.
33 minutes =3×60=180= 3 \times 60 = 180 seconds.
The initial rate is given in seconds, so the target time must also be in seconds to set up an accurate mathematical proportion.
2
Set up a direct proportion using the given rate.
1010 gallons / 1515 seconds =x= x gallons / 180180 seconds.
The pump operates at a constant rate, meaning the ratio of volume to time remains equivalent.
3
Solve for the unknown volume xx.
x=10×18015=180015=120x = \frac{10 \times 180}{15} = \frac{1800}{15} = 120 gallons.
Cross-multiplying and dividing isolates the variable, providing the total gallons transferred.

Key Concept

Direct proportions represent situations where two quantities increase at the same relative rate. When setting up proportions, it is critical to ensure that corresponding units match.
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Topics

Direct Proportions

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