Let's work through the problem step-by-step.
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Initial Capacity of the Tank: The water tank has a total capacity of 4320 gallons.
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Water Lost Due to Leak: The amount of water lost due to the leak is \( \frac{3}{8} \) of the tank's capacity: \[ \text{Water lost} = \frac{3}{8} \times 4320 = 1620 \text{ gallons} \]
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Remaining Capacity After Leak: After the leak, the remaining capacity of the tank is: \[ \text{Remaining capacity} = 4320 - 1620 = 2700 \text{ gallons} \]
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Water Filled After Leak: Now, \( \frac{2}{5} \) of the remaining capacity is filled with water: \[ \text{Water filled} = \frac{2}{5} \times 2700 = 1080 \text{ gallons} \]
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Current Water Level: The current water level in the tank is now: \[ \text{Current water level} = 1080 \text{ gallons} \]
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Water Pumped Out for Maintenance: Next, we pump out \( 0.25 \) (or \( \frac{1}{4} \)) of the current water level: \[ \text{Water pumped out} = \frac{1}{4} \times 1080 = 270 \text{ gallons} \]
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Water Left After Pumping Out: The amount of water remaining in the tank after pumping out is: \[ \text{Water remaining} = 1080 - 270 = 810 \text{ gallons} \]
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Water Contaminated and Drained: Of the remaining water, \( \frac{1}{3} \) is contaminated and needs to be drained: \[ \text{Contaminated water} = \frac{1}{3} \times 810 = 270 \text{ gallons} \]
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Final Amount of Water in the Tank: Thus, the final amount of water remaining in the tank after draining the contaminated water is: \[ \text{Final water level} = 810 - 270 = 540 \text{ gallons} \]
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Calculating the Fraction and Decimal Representation of the Original Tank Capacity: The fraction of the original tank capacity that remains is: \[ \text{Fraction remaining} = \frac{540}{4320} \] To simplify: \[ \frac{540 \div 540}{4320 \div 540} = \frac{1}{8} \]
The decimal representation of \( \frac{1}{8} \) is: \[ 0.125 \]
So, the fraction of the original tank capacity remaining is \( \frac{1}{8} \) and in decimal form, it is \( 0.125 \).
1 answer