Question

In an oil refinery, a storage tank contains 2000 gal of gasoline that initially has 100 lb of an additive dissolved in it. In preparation for winter weather, gasoline containing 2 lb of additive per gallon is pumped into the tank at a rate of 40gal min. The well-mixed solution is pumped out at a rate of 45galmin.

Answer 1

To find the amount of additive in the tank, calculate the additive entering the tank per minute and subtract the additive leaving the tank per minute. The total amount of additive in the tank will increase by approximately 77.75 lb/min.

Step-by-step explanation:

To find the amount of additive in the tank at a given time, we need to consider the flow rates of the incoming and outgoing gasoline. Let's start by calculating how much additive enters the tank per minute:

Flow rate of gasoline = 40 gal/min

Additive concentration in gasoline = 2 lb/gal

Additive entering the tank per minute = (Flow rate of gasoline) × (Additive concentration) = 40 gal/min × 2 lb/gal = 80 lb/min

Next, let's calculate how much gasoline (and additive) leaves the tank per minute:

Flow rate of outgoing gasoline = 45 gal/min

Concentration of additive in outgoing gasoline = (100 lb of additive) / (2000 gal of gasoline) = 0.05 lb/gal

Additive leaving the tank per minute = (Flow rate of outgoing gasoline) × (Concentration of additive) = 45 gal/min × 0.05 lb/gal = 2.25 lb/min

To find the amount of additive in the tank at a given time, we can subtract the amount leaving the tank per minute from the amount entering the tank per minute:

Net change in additive = (Additive entering the tank per minute) - (Additive leaving the tank per minute) = 80 lb/min - 2.25 lb/min

Therefore, the total amount of additive in the tank will increase by approximately 77.75 lb/min.