A Tank Contains 500 Liters of Brine with 10 Kg $t$

question 111

Essay

A tank contains 500 liters of brine with 10 kg of dissolved salt. Pure water enters the tank at a rate of 10 liters per minute. The well-mixed solution drains from the tank 8 liters per minute. Determine the differential equation that the amount of salt in the tank at time $t$ must satisfy.

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Definitions:

Ganglion

A structure containing a number of nerve cell bodies, typically linked by synapses, and often forming a swelling on a nerve fiber.

Arachnoid Mater

A delicate, web-like layer between the dura mater and pia mater in the brain and spinal cord, part of the meninges protecting the central nervous system.

Meninx

A term referring to any of the three membranes that cover the brain and spinal cord, including the dura mater, arachnoid mater, and pia mater.

Epidural Space

The area between the dura mater and the vertebral wall, containing fat and small blood vessels, often targeted for epidural anaesthesia.