Simultaneously, a pump drains the tank at 4 litres/second, while a mixture of 80% alcohol and 20% water is poured in at rate 3 litres/second. Thus the tank will be empty after 100 seconds. Assume that the two liquids mix thoroughly, and let y litres be the amount of alcohol in the tank after t seconds.
dy/dt = 2.4 - ( 4y / (100 - t) )
Find y as a function of t. Hence deduce that the maximum amount of alcohol in the tank occurs after about 34 seconds, and is about 39.5 litres.
* I have identified the integrating factor as A = 4 / (100 - t)
Thank you so so much if you can help!!