Question

A reservoir is filled with 1 billion cubic feet of polluted water that initially contains 0.2% pollutant. Every day 400 million cubic feet of pure water enters the reservoir and the well-mixed solution flows out at the same rate. When will the pollutant concentration in the lake be reduced to 0.1%?

Answer 1

To find the number of days it takes for the pollutant concentration in the lake to be reduced to 0.1%, set up an equation using the initial pollutant concentration, the rate of pure water entering the reservoir, and the desired pollutant concentration. Solve for the number of days.

Step-by-step explanation:

Step 1:
The pollutant concentration in the lake is initially 0.2%.

Step 2:
Every day, 400 million cubic feet of pure water enters the reservoir, so the amount of pollutant stays the same. The ratio of pollutant to the total volume of water is 0.2% / 100% = 0.002.

Step 3:
Let x be the number of days it takes for the pollutant concentration to be reduced to 0.1%. The amount of pollutant at any given time is 1 billion cubic feet * 0.002.

Step 4:
In x days, the total amount of water in the reservoir is (400 million cubic feet/day * x days) + 1 billion cubic feet.

Step 5:
The new ratio of pollutant to the total volume of water is 0.1% / 100% = 0.001.

Step 6:
Set up the equation: (1 billion cubic feet * 0.002) / ((400 million cubic feet/day * x days) + 1 billion cubic feet) = 0.001.

Step 7:
Solve the equation for x.

Step 8:
After solving the equation, you will find the value of x which represents the number of days it takes for the pollutant concentration in the lake to be reduced to 0.1%.