An aquarium filter recirculates water at a constant rate of 250 milliliters per second. Th… — SAT

An aquarium filter recirculates water at a constant rate of $250$ milliliters per second. The filter cartridge must be replaced after it has processed a total of $540$ cubic meters of water. For how many hours of continuous operation can the filter run before the cartridge must be replaced? ( $1\text{ cubic meter} = 1,000\text{ liters}$ )

Answer: 600 hours

Answer

The filter can run for

600

hours of continuous operation before the cartridge must be replaced.

To find the number of hours the filter can run, we first convert the flow rate to cubic meters per hour. The flow rate of

250

milliliters per second is equal to

0.25

liters per second. Multiplying by

3,600

seconds per hour gives a flow rate of

900

liters per hour. Since

1\text{ cubic meter} = 1,000\text{ liters}

900

liters per hour is equivalent to

0.9

cubic meters per hour. Finally, dividing the total capacity of

540

cubic meters by the flow rate of

0.9

cubic meters per hour yields a duration of

600

hours.

Step-by-Step Solution

Convert the water recirculating rate from milliliters per second to liters per second.

0.25

liters per second

To express the flow rate in terms of liters before converting to cubic meters.

Convert the rate from liters per second to liters per hour.

900

liters per hour

To align the time unit of the rate with the requested time unit (hours).

Convert the rate from liters per hour to cubic meters per hour.

0.9

cubic meters per hour

To match the volume unit of the filter cartridge capacity (cubic meters).

Divide the total cartridge capacity by the hourly flow rate of the filter.

600

hours

To find the total duration of continuous operation before replacement.

Key Concept

Unit Conversions

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