A barrel of oil is leaking into a stream that is feeding into a lake. The barrel has been leaking for 6 hours and is found still containing 300 kg of oil. Measurement of the lake were taken when the barrel was found and the concentration of oil in the water was 30 grams per cubic meter. 30 minutes later a sample showed 28 grams per cubic meter. The lake contains 50,000 cubic meters of water.

Create two differential equations, one for the barrel leaking oil, and the other for the oil in the lake.

Find the initial amount of oil in the barrel.