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Difficulty: MediumDirect Proportions

A field water purification system processes 12.512.5 gallons of clean water every 55 minutes. Operating at this same constant rate, how many gallons of clean water will the system process in 22 hours?

  1. A
    5
  2. B
    30
  3. C
    48
  4. 300Answer

Answer

The system will process 300 gallons of clean water in 2 hours.
The correct answer accurately harmonizes the time units by converting 2 hours into 120 minutes, and then scales the given volume-to-time ratio (12.512.5 gallons per 55 minutes) up to 120120 minutes, resulting in 300300 gallons.

Step-by-Step Solution

1
Convert the target time into the same units used in the given rate.
22 hours =2×60=120= 2 \times 60 = 120 minutes.
Proportions require matching units to accurately compare the two ratios.
2
Calculate the unit rate of water processed per minute.
12.5 gallons÷5 minutes=2.5 gallons per minute12.5 \text{ gallons} \div 5 \text{ minutes} = 2.5 \text{ gallons per minute}.
Finding the amount processed in one minute simplifies scaling up to the total time.
3
Multiply the unit rate by the total number of minutes.
2.5 gallons/minute×120 minutes=300 gallons2.5 \text{ gallons/minute} \times 120 \text{ minutes} = 300 \text{ gallons}.
This applies the constant rate over the entire duration to find the total volume.

Key Concept

Direct proportions with unit conversion
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Topics

Direct Proportions

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